[[ (name="C1",gens=[perm"()"],rels=Vector{Int}[[1]],nontrivrels=Vector{Int}[],orderdis=Tuple{Int,Int}[(1,1)],ordersubdis=Tuple{Int,Int}[(1,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"1",aut_gens=Vector{Vector{Int}}[[[]]],nchars=1,dims=Int[1],schur=Int[1],galrep=Int[1],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]]]) ], [ (name="C2",gens=[perm"(1,2)"],rels=Vector{Int}[[1,1]],nontrivrels=Vector{Int}[],orderdis=Tuple{Int,Int}[(1,1),(2,1)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"1",aut_gens=Vector{Vector{Int}}[[[1]]],nchars=2,dims=Int[1,1],schur=Int[1,1],galrep=Int[1,2],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]]]) ], [ (name="C3",gens=[perm"(1,3,2)"],rels=Vector{Int}[[1,1,1]],nontrivrels=Vector{Int}[],orderdis=Tuple{Int,Int}[(1,1),(3,2)],ordersubdis=Tuple{Int,Int}[(1,1),(3,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"2",aut_gens=Vector{Vector{Int}}[[[-1]]],nchars=3,dims=Int[1,1,1],schur=Int[1,1,1],galrep=Int[1,2],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]]]) ], [ (name="C4",gens=[perm"(1,4,2,3)"],rels=Vector{Int}[[1,1,1,1]],nontrivrels=Vector{Int}[],orderdis=Tuple{Int,Int}[(1,1),(2,1),(4,2)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(4,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"2",aut_gens=Vector{Vector{Int}}[[[-1]]],nchars=4,dims=Int[1,1,1,1],schur=Int[1,1,1,1],galrep=Int[1,2,3],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2^2",gens=[perm"(1,3)(2,4)",perm"(1,2)(3,4)"],rels=Vector{Int}[[1,1],[2,2],[1,2,1,2]],nontrivrels=Vector{Int}[[1,2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,3)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(4,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"6",aut_gens=Vector{Vector{Int}}[[[1,2],[2]],[[2],[1]]],nchars=4,dims=Int[1,1,1,1],schur=Int[1,1,1,1],galrep=Int[1,2,3,4],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="C5",gens=[perm"(1,5,4,3,2)"],rels=Vector{Int}[[1,1,1,1,1]],nontrivrels=Vector{Int}[],orderdis=Tuple{Int,Int}[(1,1),(5,4)],ordersubdis=Tuple{Int,Int}[(1,1),(5,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"4",aut_gens=Vector{Vector{Int}}[[[1,1]]],nchars=5,dims=Int[1,1,1,1,1],schur=Int[1,1,1,1,1],galrep=Int[1,2],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="S3",gens=[perm"(1,4)(2,5)(3,6)",perm"(1,3,2)(4,5,6)"],rels=Vector{Int}[[1,1],[2,2,2],[-2,1,-2,1]],nontrivrels=Vector{Int}[[-2,1,-2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(3,2)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(3,1),(6,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"6",aut_gens=Vector{Vector{Int}}[[[1],[-2]],[[1,2],[2]]],nchars=3,dims=Int[1,1,2],schur=Int[1,1,1],galrep=Int[1,2,3],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]]]), (name="C6",gens=[perm"(1,4)(2,5)(3,6)",perm"(1,3,2)(4,6,5)"],rels=Vector{Int}[[1,1],[2,2,2],[-2,1,2,1]],nontrivrels=Vector{Int}[[-2,1,2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(3,2),(6,2)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(3,1),(6,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"2",aut_gens=Vector{Vector{Int}}[[[1],[-2]]],nchars=6,dims=Int[1,1,1,1,1,1],schur=Int[1,1,1,1,1,1],galrep=Int[1,2,3,4],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="C7",gens=[perm"(1,7,6,5,4,3,2)"],rels=Vector{Int}[[1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[],orderdis=Tuple{Int,Int}[(1,1),(7,6)],ordersubdis=Tuple{Int,Int}[(1,1),(7,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"6",aut_gens=Vector{Vector{Int}}[[[1,1,1]]],nchars=7,dims=Int[1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1],galrep=Int[1,2],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="C8",gens=[perm"(1,8,4,6,2,7,3,5)"],rels=Vector{Int}[[1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[],orderdis=Tuple{Int,Int}[(1,1),(2,1),(4,2),(8,4)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(4,1),(8,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"4",aut_gens=Vector{Vector{Int}}[[[1,1,1,1,1]],[[1,1,1]]],nchars=8,dims=Int[1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1],galrep=Int[1,2,3,5],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*C4",gens=[perm"(1,6,2,5)(3,8,4,7)",perm"(1,3)(2,4)(5,7)(6,8)"],rels=Vector{Int}[[2,2],[1,1,1,1],[-1,2,1,2]],nontrivrels=Vector{Int}[[-1,2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(4,4)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(4,3),(8,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"8",aut_gens=Vector{Vector{Int}}[[[1],[2,-1,-1]],[[1,2],[2]]],nchars=8,dims=Int[1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="D4",gens=[perm"(1,5)(2,6)(3,7)(4,8)",perm"(1,3)(2,4)(5,8)(6,7)"],rels=Vector{Int}[[1,1],[2,2],[1,2,1,2,1,2,1,2]],nontrivrels=Vector{Int}[[1,2,1,2,1,2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,5),(4,2)],ordersubdis=Tuple{Int,Int}[(1,1),(2,5),(4,3),(8,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"8",aut_gens=Vector{Vector{Int}}[[[1],[2,1,2,1,2]],[[2],[1]]],nchars=5,dims=Int[1,1,1,1,2],schur=Int[1,1,1,1,1],galrep=Int[1,2,3,4,5],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="Q8",gens=[perm"(1,6,2,5)(3,8,4,7)",perm"(1,4,2,3)(5,7,6,8)"],rels=Vector{Int}[[-1,-1,-2,-2],[-1,-2,1,-2],[-1,-1,2,2]],nontrivrels=Vector{Int}[[-1,-1,-2,-2],[-1,-2,1,-2],[-1,-1,2,2]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(4,6)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(4,3),(8,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"24",aut_gens=Vector{Vector{Int}}[[[1,2],[2]],[[2],[1]]],nchars=5,dims=Int[1,1,1,1,2],schur=Int[1,1,1,1,2],galrep=Int[1,2,3,4,5],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2^3",gens=[perm"(1,5)(2,6)(3,7)(4,8)",perm"(1,3)(2,4)(5,7)(6,8)",perm"(1,2)(3,4)(5,6)(7,8)"],rels=Vector{Int}[[1,1],[2,2],[3,3],[1,2,1,2],[1,3,1,3],[2,3,2,3]],nontrivrels=Vector{Int}[[1,2,1,2],[1,3,1,3],[2,3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,7)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(4,7),(8,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"168",aut_gens=Vector{Vector{Int}}[[[1,2],[2],[3]],[[3],[1],[2]]],nchars=8,dims=Int[1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="C9",gens=[perm"(1,9,6,3,8,5,2,7,4)"],rels=Vector{Int}[[1,1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[],orderdis=Tuple{Int,Int}[(1,1),(3,2),(9,6)],ordersubdis=Tuple{Int,Int}[(1,1),(3,1),(9,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"6",aut_gens=Vector{Vector{Int}}[[[1,1]]],nchars=9,dims=Int[1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1],galrep=Int[1,2,4],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C3^2",gens=[perm"(1,7,4)(2,8,5)(3,9,6)",perm"(1,3,2)(4,6,5)(7,9,8)"],rels=Vector{Int}[[1,1,1],[2,2,2],[-1,-2,1,2]],nontrivrels=Vector{Int}[[-1,-2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(3,8)],ordersubdis=Tuple{Int,Int}[(1,1),(3,4),(9,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"48",aut_gens=Vector{Vector{Int}}[[[-1],[2]],[[2,-1],[-1]]],nchars=9,dims=Int[1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1],galrep=Int[1,2,4,5,6],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="D5",gens=[perm"(1,6)(2,7)(3,8)(4,9)(5,10)",perm"(1,5,4,3,2)(6,7,8,9,10)"],rels=Vector{Int}[[1,1],[-2,1,-2,1],[2,2,2,2,2]],nontrivrels=Vector{Int}[[-2,1,-2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,5),(5,4)],ordersubdis=Tuple{Int,Int}[(1,1),(2,5),(5,1),(10,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"20",aut_gens=Vector{Vector{Int}}[[[1,-2],[2]],[[1],[2,2]]],nchars=4,dims=Int[1,1,2,2],schur=Int[1,1,1,1],galrep=Int[1,2,3],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C10",gens=[perm"(1,6)(2,7)(3,8)(4,9)(5,10)",perm"(1,5,4,3,2)(6,10,9,8,7)"],rels=Vector{Int}[[1,1],[-2,1,2,1],[2,2,2,2,2]],nontrivrels=Vector{Int}[[-2,1,2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(5,4),(10,4)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(5,1),(10,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"4",aut_gens=Vector{Vector{Int}}[[[1],[-2,-2]]],nchars=10,dims=Int[1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="C11",gens=[perm"(1,11,10,9,8,7,6,5,4,3,2)"],rels=Vector{Int}[[1,1,1,1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[],orderdis=Tuple{Int,Int}[(1,1),(11,10)],ordersubdis=Tuple{Int,Int}[(1,1),(11,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"10",aut_gens=Vector{Vector{Int}}[[[1,1]]],nchars=11,dims=Int[1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="C3:C4",gens=[perm"(1,10,4,7)(2,11,5,8)(3,12,6,9)",perm"(1,3,2)(4,6,5)(7,8,9)(10,11,12)"],rels=Vector{Int}[[2,2,2],[1,1,1,1],[-1,-2,1,-2]],nontrivrels=Vector{Int}[[-1,-2,1,-2]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(3,2),(4,6),(6,2)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(3,1),(4,3),(6,1),(12,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"12",aut_gens=Vector{Vector{Int}}[[[1],[-2]],[[1,2],[2]],[[-1],[-2]]],nchars=6,dims=Int[1,1,1,1,2,2],schur=Int[1,1,1,1,2,1],galrep=Int[1,2,3,5,6],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C12",gens=[perm"(1,8,2,7)(3,10,4,9)(5,12,6,11)",perm"(1,5,3)(2,6,4)(7,11,9)(8,12,10)"],rels=Vector{Int}[[2,2,2],[1,1,1,1],[-1,-2,1,2]],nontrivrels=Vector{Int}[[-1,-2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(3,2),(4,2),(6,2),(12,4)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(3,1),(4,1),(6,1),(12,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"4",aut_gens=Vector{Vector{Int}}[[[1],[-2]],[[-1],[-2]]],nchars=12,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,5,6,7],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="A4",gens=[perm"(1,9,5)(2,10,6)(3,11,7)(4,12,8)",perm"(1,2)(3,4)(5,8)(6,7)(9,11)(10,12)"],rels=Vector{Int}[[2,2],[1,1,1],[2,-1,2,-1,2,-1]],nontrivrels=Vector{Int}[[2,-1,2,-1,2,-1]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(3,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(3,4),(4,1),(12,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"24",aut_gens=Vector{Vector{Int}}[[[1],[1,2,-1,2]],[[1,2],[2]],[[-1],[1,2,-1]]],nchars=4,dims=Int[1,1,1,3],schur=Int[1,1,1,1],galrep=Int[1,2,4],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]]]), (name="D6",gens=[perm"(1,7)(2,8)(3,9)(4,10)(5,11)(6,12)",perm"(1,4)(2,5)(3,6)(7,10)(8,11)(9,12)",perm"(1,3,2)(4,6,5)(7,8,9)(10,11,12)"],rels=Vector{Int}[[1,1],[2,2],[3,3,3],[1,2,1,2],[1,-3,1,-3],[2,-3,2,3]],nontrivrels=Vector{Int}[[1,2,1,2],[1,-3,1,-3],[2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(3,2),(6,2)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(3,1),(4,3),(6,3),(12,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"12",aut_gens=Vector{Vector{Int}}[[[1],[2],[-3]],[[1,3],[2],[3]],[[1,2],[2],[-3]]],nchars=6,dims=Int[1,1,1,1,2,2],schur=Int[1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*C6",gens=[perm"(1,7)(2,8)(3,9)(4,10)(5,11)(6,12)",perm"(1,4)(2,5)(3,6)(7,10)(8,11)(9,12)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)"],rels=Vector{Int}[[1,1],[2,2],[3,3,3],[1,2,1,2],[1,-3,1,3],[2,-3,2,3]],nontrivrels=Vector{Int}[[1,2,1,2],[1,-3,1,3],[2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(3,2),(6,6)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(3,1),(4,1),(6,3),(12,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"12",aut_gens=Vector{Vector{Int}}[[[1],[2],[-3]],[[1,2],[2],[-3]],[[2],[1],[-3]]],nchars=12,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="C13",gens=[perm"(1,13,12,11,10,9,8,7,6,5,4,3,2)"],rels=Vector{Int}[[1,1,1,1,1,1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[],orderdis=Tuple{Int,Int}[(1,1),(13,12)],ordersubdis=Tuple{Int,Int}[(1,1),(13,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"12",aut_gens=Vector{Vector{Int}}[[[1,1]]],nchars=13,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="D7",gens=[perm"(1,8)(2,9)(3,10)(4,11)(5,12)(6,13)(7,14)",perm"(1,7,6,5,4,3,2)(8,9,10,11,12,13,14)"],rels=Vector{Int}[[1,1],[-2,1,-2,1],[2,2,2,2,2,2,2]],nontrivrels=Vector{Int}[[-2,1,-2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(7,6)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(7,1),(14,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"42",aut_gens=Vector{Vector{Int}}[[[1,-2,-2,-2],[2]],[[1],[-2,-2]]],nchars=5,dims=Int[1,1,2,2,2],schur=Int[1,1,1,1,1],galrep=Int[1,2,3],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C14",gens=[perm"(1,8)(2,9)(3,10)(4,11)(5,12)(6,13)(7,14)",perm"(1,7,6,5,4,3,2)(8,14,13,12,11,10,9)"],rels=Vector{Int}[[1,1],[-2,1,2,1],[2,2,2,2,2,2,2]],nontrivrels=Vector{Int}[[-2,1,2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(7,6),(14,6)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(7,1),(14,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"6",aut_gens=Vector{Vector{Int}}[[[1],[2,2,2]]],nchars=14,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="C15",gens=[perm"(1,11,6)(2,12,7)(3,13,8)(4,14,9)(5,15,10)",perm"(1,5,4,3,2)(6,10,9,8,7)(11,15,14,13,12)"],rels=Vector{Int}[[1,1,1],[-1,-2,1,2],[2,2,2,2,2]],nontrivrels=Vector{Int}[[-1,-2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(3,2),(5,4),(15,8)],ordersubdis=Tuple{Int,Int}[(1,1),(3,1),(5,1),(15,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"8",aut_gens=Vector{Vector{Int}}[[[1],[-2,-2]],[[-1],[-2]]],nchars=15,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,4,5],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="C16",gens=[perm"(1,16,8,12,4,14,6,10,2,15,7,11,3,13,5,9)"],rels=Vector{Int}[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[],orderdis=Tuple{Int,Int}[(1,1),(2,1),(4,2),(8,4),(16,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(4,1),(8,1),(16,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"8",aut_gens=Vector{Vector{Int}}[[[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1]],[[1,1,1]]],nchars=16,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,5,9],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C4^2",gens=[perm"(1,11,3,9)(2,12,4,10)(5,15,7,13)(6,16,8,14)",perm"(1,6,2,5)(3,8,4,7)(9,14,10,13)(11,16,12,15)"],rels=Vector{Int}[[1,1,1,1],[2,2,2,2],[-1,-2,1,2]],nontrivrels=Vector{Int}[[-1,-2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(4,12)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(4,7),(8,3),(16,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"96",aut_gens=Vector{Vector{Int}}[[[1,2],[2]],[[2],[1]]],nchars=16,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,5,6,7,8,9,10,11],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2^2:C4",gens=[perm"(1,10,2,9)(3,12,4,11)(5,14,6,13)(7,16,8,15)",perm"(1,5)(2,6)(3,7)(4,8)(9,15)(10,16)(11,13)(12,14)"],rels=Vector{Int}[[2,2],[1,1,1,1],[-1,2,1,1,2,-1],[-1,2,1,2,-1,2,1,2]],nontrivrels=Vector{Int}[[-1,2,1,1,2,-1],[-1,2,1,2,-1,2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(4,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(4,11),(8,3),(16,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"32",aut_gens=Vector{Vector{Int}}[[[1],[2,1,2,-1,2]],[[1],[2,-1,-1]],[[1,2],[2]]],nchars=10,dims=Int[1,1,1,1,1,1,1,1,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,9,10],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C4:C4",gens=[perm"(1,10,2,9)(3,12,4,11)(5,14,6,13)(7,16,8,15)",perm"(1,7,3,5)(2,8,4,6)(9,13,11,15)(10,14,12,16)"],rels=Vector{Int}[[2,2,2,2],[1,1,1,1],[-1,-2,1,-2]],nontrivrels=Vector{Int}[[-1,-2,1,-2]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(4,12)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(4,7),(8,3),(16,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"32",aut_gens=Vector{Vector{Int}}[[[1],[-2]],[[1],[2,-1,-1]],[[1,2],[2]]],nchars=10,dims=Int[1,1,1,1,1,1,1,1,2,2],schur=Int[1,1,1,1,1,1,1,1,2,1],galrep=Int[1,2,3,4,5,6,9,10],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*C8",gens=[perm"(1,12,4,10,2,11,3,9)(5,16,8,14,6,15,7,13)",perm"(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)"],rels=Vector{Int}[[2,2],[-1,2,1,2],[1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[[-1,2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(4,4),(8,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(4,3),(8,3),(16,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"16",aut_gens=Vector{Vector{Int}}[[[1],[2,1,1,1,1]],[[1,1,1],[2]],[[1,2],[2]]],nchars=16,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,9,10],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="OD16",gens=[perm"(1,12,4,10,2,11,3,9)(5,16,8,14,6,15,7,13)",perm"(1,5)(2,6)(3,7)(4,8)(9,14)(10,13)(11,16)(12,15)"],rels=Vector{Int}[[2,2],[-1,-1,-1,2,-1,2],[1,2,1,2,1,1],[-1,-1,-1,-1,2,1,2,-1]],nontrivrels=Vector{Int}[[-1,-1,-1,2,-1,2],[1,2,1,2,1,1],[-1,-1,-1,-1,2,1,2,-1]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(4,4),(8,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(4,3),(8,3),(16,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"16",aut_gens=Vector{Vector{Int}}[[[1],[2,1,1,1,1]],[[1,1,1],[2]],[[1,2],[2]]],nchars=10,dims=Int[1,1,1,1,1,1,1,1,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,9],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="D8",gens=[perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)",perm"(1,5)(2,6)(3,7)(4,8)(9,15)(10,16)(11,14)(12,13)"],rels=Vector{Int}[[1,1],[2,2],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1]],nontrivrels=Vector{Int}[[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,9),(4,2),(8,4)],ordersubdis=Tuple{Int,Int}[(1,1),(2,9),(4,5),(8,3),(16,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"32",aut_gens=Vector{Vector{Int}}[[[1],[2,1,1,2,1,2,1]],[[1,1,2,1,2,1,2,1,2],[2]],[[2],[1]]],nchars=7,dims=Int[1,1,1,1,2,2,2],schur=Int[1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="SD16",gens=[perm"(1,10,2,9)(3,12,4,11)(5,14,6,13)(7,16,8,15)",perm"(1,5)(2,6)(3,7)(4,8)(9,15)(10,16)(11,14)(12,13)"],rels=Vector{Int}[[2,2],[1,2,1,1,2,1],[1,2,1,2,-1,2,1,2]],nontrivrels=Vector{Int}[[1,2,1,1,2,1],[1,2,1,2,-1,2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,5),(4,6),(8,4)],ordersubdis=Tuple{Int,Int}[(1,1),(2,5),(4,5),(8,3),(16,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"16",aut_gens=Vector{Vector{Int}}[[[1],[2,-1,2,-1,2]],[[1,-2,1,-2,1],[2]],[[-1],[2]]],nchars=7,dims=Int[1,1,1,1,2,2,2],schur=Int[1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="Q16",gens=[perm"(1,10,2,9)(3,12,4,11)(5,14,6,13)(7,16,8,15)",perm"(1,6,2,5)(3,8,4,7)(9,16,10,15)(11,13,12,14)"],rels=Vector{Int}[[-1,-1,2,2],[1,1,1,1],[1,1,1,1],[2,-1,-2,1,-2,1,-2,-1]],nontrivrels=Vector{Int}[[-1,-1,2,2],[2,-1,-2,1,-2,1,-2,-1]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(4,10),(8,4)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(4,5),(8,3),(16,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"32",aut_gens=Vector{Vector{Int}}[[[1],[2,-1,-2,-1,2]],[[-1],[2]],[[2],[1]]],nchars=7,dims=Int[1,1,1,1,2,2,2],schur=Int[1,1,1,1,1,2,2],galrep=Int[1,2,3,4,5,6],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2^2*C4",gens=[perm"(1,10,2,9)(3,12,4,11)(5,14,6,13)(7,16,8,15)",perm"(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)",perm"(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16)"],rels=Vector{Int}[[2,2],[3,3],[1,1,1,1],[-1,2,1,2],[-1,3,1,3],[2,3,2,3]],nontrivrels=Vector{Int}[[-1,2,1,2],[-1,3,1,3],[2,3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(4,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(4,11),(8,7),(16,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"192",aut_gens=Vector{Vector{Int}}[[[1],[2],[3,-1,-1]],[[1,2],[2],[3]],[[1],[2,3],[3]],[[1,2],[2],[2,3]]],nchars=16,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*D4",gens=[perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)",perm"(1,5)(2,6)(3,7)(4,8)(9,14)(10,13)(11,16)(12,15)",perm"(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16)"],rels=Vector{Int}[[1,1],[2,2],[3,3],[1,3,1,3],[2,3,2,3],[1,2,1,2,1,2,1,2]],nontrivrels=Vector{Int}[[1,3,1,3],[2,3,2,3],[1,2,1,2,1,2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,11),(4,4)],ordersubdis=Tuple{Int,Int}[(1,1),(2,11),(4,15),(8,7),(16,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"64",aut_gens=Vector{Vector{Int}}[[[1],[2],[3,1,2,1,2]],[[1,3],[2],[3]],[[2],[1],[3]]],nchars=10,dims=Int[1,1,1,1,1,1,1,1,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*Q8",gens=[perm"(1,10,2,9)(3,12,4,11)(5,14,6,13)(7,16,8,15)",perm"(1,6,2,5)(3,8,4,7)(9,13,10,14)(11,15,12,16)",perm"(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16)"],rels=Vector{Int}[[3,3],[-1,-1,-2,-2],[-1,-2,1,-2],[-1,-1,2,2],[-1,3,1,3],[-2,3,2,3]],nontrivrels=Vector{Int}[[-1,-1,-2,-2],[-1,-2,1,-2],[-1,-1,2,2],[-1,3,1,3],[-2,3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(4,12)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(4,7),(8,7),(16,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"192",aut_gens=Vector{Vector{Int}}[[[1],[2],[3,-1,-1]],[[1,3],[2],[3]],[[1,2],[2],[3]],[[2],[1],[3]]],nchars=10,dims=Int[1,1,1,1,1,1,1,1,2,2],schur=Int[1,1,1,1,1,1,1,1,2,2],galrep=Int[1,2,3,4,5,6,7,8,9,10],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="D4:C2",gens=[perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)",perm"(1,5)(2,6)(3,7)(4,8)(9,14)(10,13)(11,16)(12,15)",perm"(1,4,2,3)(5,8,6,7)(9,12,10,11)(13,16,14,15)"],rels=Vector{Int}[[1,1],[2,2],[3,3,3,3],[1,-3,1,3],[2,-3,2,3],[1,2,3,3,1,2]],nontrivrels=Vector{Int}[[1,-3,1,3],[2,-3,2,3],[1,2,3,3,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(4,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(4,7),(8,7),(16,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"48",aut_gens=Vector{Vector{Int}}[[[1],[2],[-3]],[[2],[1],[3]],[[1,2,3],[2],[3]]],nchars=10,dims=Int[1,1,1,1,1,1,1,1,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2^4",gens=[perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)",perm"(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)",perm"(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16)",perm"(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)"],rels=Vector{Int}[[1,1],[2,2],[3,3],[4,4],[1,2,1,2],[1,3,1,3],[2,3,2,3],[1,4,1,4],[2,4,2,4],[3,4,3,4]],nontrivrels=Vector{Int}[[1,2,1,2],[1,3,1,3],[2,3,2,3],[1,4,1,4],[2,4,2,4],[3,4,3,4]],orderdis=Tuple{Int,Int}[(1,1),(2,15)],ordersubdis=Tuple{Int,Int}[(1,1),(2,15),(4,35),(8,15),(16,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"20160",aut_gens=Vector{Vector{Int}}[[[4],[1],[2],[3]],[[1],[2],[3],[1,4]]],nchars=16,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="C17",gens=[perm"(1,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2)"],rels=Vector{Int}[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[],orderdis=Tuple{Int,Int}[(1,1),(17,16)],ordersubdis=Tuple{Int,Int}[(1,1),(17,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"16",aut_gens=Vector{Vector{Int}}[[[1,1,1]]],nchars=17,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="D9",gens=[perm"(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17)(9,18)",perm"(1,9,6,3,8,5,2,7,4)(10,13,16,11,14,17,12,15,18)"],rels=Vector{Int}[[1,1],[-2,1,-2,1],[2,2,2,2,2,2,2,2,2]],nontrivrels=Vector{Int}[[-2,1,-2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,9),(3,2),(9,6)],ordersubdis=Tuple{Int,Int}[(1,1),(2,9),(3,1),(6,3),(9,1),(18,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"54",aut_gens=Vector{Vector{Int}}[[[1],[-2]],[[1,-2,-2,-2,-2,-2],[2]],[[1],[-2,-2,-2,-2,-2]]],nchars=6,dims=Int[1,1,2,2,2,2],schur=Int[1,1,1,1,1,1],galrep=Int[1,2,3,4],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C18",gens=[perm"(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17)(9,18)",perm"(1,9,6,3,8,5,2,7,4)(10,18,15,12,17,14,11,16,13)"],rels=Vector{Int}[[1,1],[-2,1,2,1],[2,2,2,2,2,2,2,2,2]],nontrivrels=Vector{Int}[[-2,1,2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(3,2),(6,2),(9,6),(18,6)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(3,1),(6,1),(9,1),(18,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"6",aut_gens=Vector{Vector{Int}}[[[1],[2,2]]],nchars=18,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,7,8],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C3*S3",gens=[perm"(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17)(9,18)",perm"(1,7,4)(2,8,5)(3,9,6)(10,16,13)(11,17,14)(12,18,15)",perm"(1,3,2)(4,6,5)(7,9,8)(10,11,12)(13,14,15)(16,17,18)"],rels=Vector{Int}[[1,1],[2,2,2],[3,3,3],[-2,1,2,1],[-2,-3,2,3],[1,-3,1,-3]],nontrivrels=Vector{Int}[[-2,1,2,1],[-2,-3,2,3],[1,-3,1,-3]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(3,8),(6,6)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(3,4),(6,4),(9,1),(18,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"12",aut_gens=Vector{Vector{Int}}[[[1],[2],[-3]],[[1,3],[2],[3]],[[1],[-2],[-3]]],nchars=9,dims=Int[1,1,1,1,1,1,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,7,8],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C3:S3",gens=[perm"(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17)(9,18)",perm"(1,7,4)(2,8,5)(3,9,6)(10,13,16)(11,14,17)(12,15,18)",perm"(1,3,2)(4,6,5)(7,9,8)(10,11,12)(13,14,15)(16,17,18)"],rels=Vector{Int}[[1,1],[2,2,2],[3,3,3],[-2,1,-2,1],[-2,-3,2,3],[1,-3,1,-3]],nontrivrels=Vector{Int}[[-2,1,-2,1],[-2,-3,2,3],[1,-3,1,-3]],orderdis=Tuple{Int,Int}[(1,1),(2,9),(3,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,9),(3,4),(6,12),(9,1),(18,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"432",aut_gens=Vector{Vector{Int}}[[[1,2],[2],[3]],[[1],[-2],[3]],[[1],[-2,-3],[2]]],nchars=6,dims=Int[1,1,2,2,2,2],schur=Int[1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C3*C6",gens=[perm"(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17)(9,18)",perm"(1,7,4)(2,8,5)(3,9,6)(10,16,13)(11,17,14)(12,18,15)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)"],rels=Vector{Int}[[1,1],[2,2,2],[3,3,3],[-2,1,2,1],[-2,-3,2,3],[1,-3,1,3]],nontrivrels=Vector{Int}[[-2,1,2,1],[-2,-3,2,3],[1,-3,1,3]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(3,8),(6,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(3,4),(6,4),(9,1),(18,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"48",aut_gens=Vector{Vector{Int}}[[[1],[-2,-3],[2]],[[1],[-2],[3]]],nchars=18,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,7,8,9,10,11,12],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="C19",gens=[perm"(1,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2)"],rels=Vector{Int}[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[],orderdis=Tuple{Int,Int}[(1,1),(19,18)],ordersubdis=Tuple{Int,Int}[(1,1),(19,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"18",aut_gens=Vector{Vector{Int}}[[[1,1]]],nchars=19,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="C5:C4",gens=[perm"(1,16,6,11)(2,17,7,12)(3,18,8,13)(4,19,9,14)(5,20,10,15)",perm"(1,5,4,3,2)(6,10,9,8,7)(11,12,13,14,15)(16,17,18,19,20)"],rels=Vector{Int}[[1,1,1,1],[-1,-2,1,-2],[2,2,2,2,2]],nontrivrels=Vector{Int}[[-1,-2,1,-2]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(4,10),(5,4),(10,4)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(4,5),(5,1),(10,1),(20,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"40",aut_gens=Vector{Vector{Int}}[[[1,-2],[2]],[[1],[2,2]],[[-1],[-2]]],nchars=8,dims=Int[1,1,1,1,2,2,2,2],schur=Int[1,1,1,1,2,1,1,2],galrep=Int[1,2,3,5,6],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C20",gens=[perm"(1,12,2,11)(3,14,4,13)(5,16,6,15)(7,18,8,17)(9,20,10,19)",perm"(1,9,7,5,3)(2,10,8,6,4)(11,19,17,15,13)(12,20,18,16,14)"],rels=Vector{Int}[[1,1,1,1],[-1,-2,1,2],[2,2,2,2,2]],nontrivrels=Vector{Int}[[-1,-2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(4,2),(5,4),(10,4),(20,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(4,1),(5,1),(10,1),(20,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"8",aut_gens=Vector{Vector{Int}}[[[1],[2,2]],[[-1],[-2]]],nchars=20,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,5,6,7],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="F5",gens=[perm"(1,16,6,11)(2,17,7,12)(3,18,8,13)(4,19,9,14)(5,20,10,15)",perm"(1,5,4,3,2)(6,7,8,9,10)(11,14,12,15,13)(16,18,20,17,19)"],rels=Vector{Int}[[1,1,1,1],[1,-2,-1,-2,-2],[1,1,-2,-1,-1,-2]],nontrivrels=Vector{Int}[[1,-2,-1,-2,-2],[1,1,-2,-1,-1,-2]],orderdis=Tuple{Int,Int}[(1,1),(2,5),(4,10),(5,4)],ordersubdis=Tuple{Int,Int}[(1,1),(2,5),(4,5),(5,1),(10,1),(20,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"20",aut_gens=Vector{Vector{Int}}[[[1],[2,2]],[[1,2],[2]]],nchars=5,dims=Int[1,1,1,1,4],schur=Int[1,1,1,1,1],galrep=Int[1,2,3,5],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="D10",gens=[perm"(1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20)",perm"(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20)",perm"(1,5,4,3,2)(6,10,9,8,7)(11,12,13,14,15)(16,17,18,19,20)"],rels=Vector{Int}[[1,1],[2,2],[1,2,1,2],[1,-3,1,-3],[2,-3,2,3],[3,3,3,3,3]],nontrivrels=Vector{Int}[[1,2,1,2],[1,-3,1,-3],[2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,11),(5,4),(10,4)],ordersubdis=Tuple{Int,Int}[(1,1),(2,11),(4,5),(5,1),(10,3),(20,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"40",aut_gens=Vector{Vector{Int}}[[[1,-3],[2],[3]],[[1],[2],[-3,-3]],[[1,2],[2],[-3]]],nchars=8,dims=Int[1,1,1,1,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*C10",gens=[perm"(1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20)",perm"(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20)",perm"(1,5,4,3,2)(6,10,9,8,7)(11,15,14,13,12)(16,20,19,18,17)"],rels=Vector{Int}[[1,1],[2,2],[1,2,1,2],[1,-3,1,3],[2,-3,2,3],[3,3,3,3,3]],nontrivrels=Vector{Int}[[1,2,1,2],[1,-3,1,3],[2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(5,4),(10,12)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(4,1),(5,1),(10,3),(20,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"24",aut_gens=Vector{Vector{Int}}[[[1],[2],[-3,-3]],[[1,2],[2],[-3]],[[2],[1],[-3]]],nchars=20,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="C7:C3",gens=[perm"(1,15,8)(2,16,9)(3,17,10)(4,18,11)(5,19,12)(6,20,13)(7,21,14)",perm"(1,7,6,5,4,3,2)(8,13,11,9,14,12,10)(15,18,21,17,20,16,19)"],rels=Vector{Int}[[1,1,1],[-2,-2,-1,2,1]],nontrivrels=Vector{Int}[[-2,-2,-1,2,1]],orderdis=Tuple{Int,Int}[(1,1),(3,14),(7,6)],ordersubdis=Tuple{Int,Int}[(1,1),(3,7),(7,1),(21,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"42",aut_gens=Vector{Vector{Int}}[[[1,2],[2]],[[1],[-2,-2]]],nchars=5,dims=Int[1,1,1,3,3],schur=Int[1,1,1,1,1],galrep=Int[1,2,4],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C21",gens=[perm"(1,15,8)(2,16,9)(3,17,10)(4,18,11)(5,19,12)(6,20,13)(7,21,14)",perm"(1,7,6,5,4,3,2)(8,14,13,12,11,10,9)(15,21,20,19,18,17,16)"],rels=Vector{Int}[[1,1,1],[-1,-2,1,2],[2,2,2,2,2,2,2]],nontrivrels=Vector{Int}[[-1,-2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(3,2),(7,6),(21,12)],ordersubdis=Tuple{Int,Int}[(1,1),(3,1),(7,1),(21,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"12",aut_gens=Vector{Vector{Int}}[[[1],[-2,-2]],[[-1],[-2]]],nchars=21,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,4,5],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="D11",gens=[perm"(1,12)(2,13)(3,14)(4,15)(5,16)(6,17)(7,18)(8,19)(9,20)(10,21)(11,22)",perm"(1,11,10,9,8,7,6,5,4,3,2)(12,13,14,15,16,17,18,19,20,21,22)"],rels=Vector{Int}[[1,1],[-2,1,-2,1],[2,2,2,2,2,2,2,2,2,2,2]],nontrivrels=Vector{Int}[[-2,1,-2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,11),(11,10)],ordersubdis=Tuple{Int,Int}[(1,1),(2,11),(11,1),(22,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"110",aut_gens=Vector{Vector{Int}}[[[1,2,2,2,2],[2]],[[1],[-2,-2,-2]]],nchars=7,dims=Int[1,1,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1],galrep=Int[1,2,3],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C22",gens=[perm"(1,12)(2,13)(3,14)(4,15)(5,16)(6,17)(7,18)(8,19)(9,20)(10,21)(11,22)",perm"(1,11,10,9,8,7,6,5,4,3,2)(12,22,21,20,19,18,17,16,15,14,13)"],rels=Vector{Int}[[1,1],[-2,1,2,1],[2,2,2,2,2,2,2,2,2,2,2]],nontrivrels=Vector{Int}[[-2,1,2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(11,10),(22,10)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(11,1),(22,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"10",aut_gens=Vector{Vector{Int}}[[[1],[-2,-2,-2,-2,-2]]],nchars=22,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="C23",gens=[perm"(1,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2)"],rels=Vector{Int}[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[],orderdis=Tuple{Int,Int}[(1,1),(23,22)],ordersubdis=Tuple{Int,Int}[(1,1),(23,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"22",aut_gens=Vector{Vector{Int}}[[[1,1,1,1,1]]],nchars=23,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="C3:C8",gens=[perm"(1,22,10,16,4,19,7,13)(2,23,11,17,5,20,8,14)(3,24,12,18,6,21,9,15)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,14,15)(16,17,18)(19,20,21)(22,23,24)"],rels=Vector{Int}[[2,2,2],[-1,-2,1,-2],[1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[[-1,-2,1,-2]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(3,2),(4,2),(6,2),(8,12),(12,4)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(3,1),(4,1),(6,1),(8,3),(12,1),(24,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"24",aut_gens=Vector{Vector{Int}}[[[1],[-2]],[[1,2],[2]],[[1,1,1,1,1],[-2]],[[1,1,1],[-2]]],nchars=12,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,2,1,1,1],galrep=Int[1,2,3,5,9,10,11],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C24",gens=[perm"(1,16,4,14,2,15,3,13)(5,20,8,18,6,19,7,17)(9,24,12,22,10,23,11,21)",perm"(1,9,5)(2,10,6)(3,11,7)(4,12,8)(13,21,17)(14,22,18)(15,23,19)(16,24,20)"],rels=Vector{Int}[[2,2,2],[-1,-2,1,2],[1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[[-1,-2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(3,2),(4,2),(6,2),(8,4),(12,4),(24,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(3,1),(4,1),(6,1),(8,1),(12,1),(24,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"8",aut_gens=Vector{Vector{Int}}[[[1],[-2]],[[1,1,1,1,1],[-2]],[[1,1,1],[-2]]],nchars=24,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,5,9,10,11,13],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="SL(2,3)",gens=[perm"(1,17,9)(2,18,10)(3,19,11)(4,20,12)(5,21,13)(6,22,14)(7,23,15)(8,24,16)",perm"(1,4,2,3)(5,7,6,8)(9,16,10,15)(11,13,12,14)(17,22,18,21)(19,24,20,23)"],rels=Vector{Int}[[1,1,1],[2,2,2,2],[2,-1,-2,-2,1,2],[-2,-1,2,-1,2,-1]],nontrivrels=Vector{Int}[[2,-1,-2,-2,1,2],[-2,-1,2,-1,2,-1]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(3,8),(4,6),(6,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(3,4),(4,3),(6,4),(8,1),(24,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"24",aut_gens=Vector{Vector{Int}}[[[1],[1,-2,-2,-2,-1,2]],[[1,2],[-2]],[[-1],[1,2,2,2,-1]]],nchars=7,dims=Int[1,1,1,2,2,2,3],schur=Int[1,1,1,2,1,1,1],galrep=Int[1,2,4,5,7],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C3:Q8",gens=[perm"(1,16,4,13)(2,17,5,14)(3,18,6,15)(7,22,10,19)(8,23,11,20)(9,24,12,21)",perm"(1,10,4,7)(2,11,5,8)(3,12,6,9)(13,19,16,22)(14,20,17,23)(15,21,18,24)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,14,15)(16,17,18)(19,20,21)(22,23,24)"],rels=Vector{Int}[[3,3,3],[-1,-1,-2,-2],[-1,-2,1,-2],[-1,-1,2,2],[-1,-3,1,-3],[-2,-3,2,3]],nontrivrels=Vector{Int}[[-1,-1,-2,-2],[-1,-2,1,-2],[-1,-1,2,2],[-1,-3,1,-3],[-2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(3,2),(4,14),(6,2),(12,4)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(3,1),(4,7),(6,1),(8,3),(12,3),(24,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"48",aut_gens=Vector{Vector{Int}}[[[1],[-2],[-3]],[[1,-3],[2],[3]],[[1],[2],[-3]],[[1,2],[2],[-3]]],nchars=9,dims=Int[1,1,1,1,2,2,2,2,2],schur=Int[1,1,1,1,1,1,2,2,2],galrep=Int[1,2,3,4,5,6,7,8],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C4*S3",gens=[perm"(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)",perm"(1,10,4,7)(2,11,5,8)(3,12,6,9)(13,22,16,19)(14,23,17,20)(15,24,18,21)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,14,15)(16,17,18)(19,20,21)(22,23,24)"],rels=Vector{Int}[[1,1],[3,3,3],[2,2,2,2],[-2,1,2,1],[-2,-3,2,3],[1,-3,1,-3]],nontrivrels=Vector{Int}[[-2,1,2,1],[-2,-3,2,3],[1,-3,1,-3]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(3,2),(4,8),(6,2),(12,4)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(3,1),(4,7),(6,3),(8,3),(12,3),(24,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"24",aut_gens=Vector{Vector{Int}}[[[1],[2],[-3]],[[1,3],[2],[3]],[[1,-2,-2],[2],[-3]],[[1],[-2],[-3]]],nchars=12,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,9,10,11],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="D12",gens=[perm"(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)",perm"(1,10,4,7)(2,11,5,8)(3,12,6,9)(13,19,16,22)(14,20,17,23)(15,21,18,24)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,14,15)(16,17,18)(19,20,21)(22,23,24)"],rels=Vector{Int}[[1,1],[3,3,3],[2,2,2,2],[-2,1,-2,1],[-2,-3,2,3],[1,-3,1,-3]],nontrivrels=Vector{Int}[[-2,1,-2,1],[-2,-3,2,3],[1,-3,1,-3]],orderdis=Tuple{Int,Int}[(1,1),(2,13),(3,2),(4,2),(6,2),(12,4)],ordersubdis=Tuple{Int,Int}[(1,1),(2,13),(3,1),(4,7),(6,5),(8,3),(12,3),(24,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"48",aut_gens=Vector{Vector{Int}}[[[1],[-2],[-3]],[[1,-3],[2],[3]],[[1],[2],[-3]],[[1,2],[2],[-3]]],nchars=9,dims=Int[1,1,1,1,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*C3:C4",gens=[perm"(1,16,4,13)(2,17,5,14)(3,18,6,15)(7,22,10,19)(8,23,11,20)(9,24,12,21)",perm"(1,7)(2,8)(3,9)(4,10)(5,11)(6,12)(13,19)(14,20)(15,21)(16,22)(17,23)(18,24)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,14,15)(16,17,18)(19,20,21)(22,23,24)"],rels=Vector{Int}[[2,2],[3,3,3],[1,1,1,1],[-1,2,1,2],[-1,-3,1,-3],[2,-3,2,3]],nontrivrels=Vector{Int}[[-1,2,1,2],[-1,-3,1,-3],[2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(3,2),(4,12),(6,6)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(3,1),(4,7),(6,3),(8,3),(12,3),(24,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"48",aut_gens=Vector{Vector{Int}}[[[1],[2],[-3]],[[1,3],[2],[3]],[[1],[2,-1,-1],[-3]],[[1,2],[2],[-3]]],nchars=12,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,2,1,2,1],galrep=Int[1,2,3,4,5,6,9,10,11,12],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C3:D4",gens=[perm"(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)",perm"(1,7)(2,8)(3,9)(4,10)(5,11)(6,12)(13,22)(14,23)(15,24)(16,19)(17,20)(18,21)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,14,15)(16,17,18)(19,20,21)(22,23,24)"],rels=Vector{Int}[[1,1],[2,2],[3,3,3],[1,-3,1,-3],[2,-3,2,3],[1,2,1,2,1,2,1,2]],nontrivrels=Vector{Int}[[1,-3,1,-3],[2,-3,2,3],[1,2,1,2,1,2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,9),(3,2),(4,6),(6,6)],ordersubdis=Tuple{Int,Int}[(1,1),(2,9),(3,1),(4,7),(6,5),(8,3),(12,3),(24,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"24",aut_gens=Vector{Vector{Int}}[[[1],[2,1,2,1,2],[-3]],[[1,1,2,1,2],[2],[3]],[[1,-3],[2],[3]],[[1],[2],[-3]]],nchars=9,dims=Int[1,1,1,1,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*C12",gens=[perm"(1,14,2,13)(3,16,4,15)(5,18,6,17)(7,20,8,19)(9,22,10,21)(11,24,12,23)",perm"(1,7)(2,8)(3,9)(4,10)(5,11)(6,12)(13,19)(14,20)(15,21)(16,22)(17,23)(18,24)",perm"(1,5,3)(2,6,4)(7,11,9)(8,12,10)(13,17,15)(14,18,16)(19,23,21)(20,24,22)"],rels=Vector{Int}[[2,2],[3,3,3],[1,1,1,1],[-1,2,1,2],[-1,-3,1,3],[2,-3,2,3]],nontrivrels=Vector{Int}[[-1,2,1,2],[-1,-3,1,3],[2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(3,2),(4,4),(6,6),(12,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(3,1),(4,3),(6,3),(8,1),(12,3),(24,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"16",aut_gens=Vector{Vector{Int}}[[[1],[2],[-3]],[[1],[2,-1,-1],[-3]],[[1,2],[2],[-3]]],nchars=24,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,9,10,11,12,13,14],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C3*D4",gens=[perm"(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)",perm"(1,7)(2,8)(3,9)(4,10)(5,11)(6,12)(13,20)(14,19)(15,22)(16,21)(17,24)(18,23)",perm"(1,5,3)(2,6,4)(7,11,9)(8,12,10)(13,17,15)(14,18,16)(19,23,21)(20,24,22)"],rels=Vector{Int}[[1,1],[2,2],[3,3,3],[1,-3,1,3],[2,-3,2,3],[1,2,1,2,1,2,1,2]],nontrivrels=Vector{Int}[[1,-3,1,3],[2,-3,2,3],[1,2,1,2,1,2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,5),(3,2),(4,2),(6,10),(12,4)],ordersubdis=Tuple{Int,Int}[(1,1),(2,5),(3,1),(4,3),(6,5),(8,1),(12,3),(24,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"16",aut_gens=Vector{Vector{Int}}[[[1],[2,1,2,1,2],[3]],[[1],[2],[-3]],[[2],[1],[-3]]],nchars=15,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,9,13,14],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C3*Q8",gens=[perm"(1,14,2,13)(3,16,4,15)(5,18,6,17)(7,20,8,19)(9,22,10,21)(11,24,12,23)",perm"(1,8,2,7)(3,10,4,9)(5,12,6,11)(13,19,14,20)(15,21,16,22)(17,23,18,24)",perm"(1,5,3)(2,6,4)(7,11,9)(8,12,10)(13,17,15)(14,18,16)(19,23,21)(20,24,22)"],rels=Vector{Int}[[3,3,3],[-1,-1,-2,-2],[-1,-2,1,-2],[-1,-1,2,2],[-1,-3,1,3],[-2,-3,2,3]],nontrivrels=Vector{Int}[[-1,-1,-2,-2],[-1,-2,1,-2],[-1,-1,2,2],[-1,-3,1,3],[-2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(3,2),(4,6),(6,2),(12,12)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(3,1),(4,3),(6,1),(8,1),(12,3),(24,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"48",aut_gens=Vector{Vector{Int}}[[[1],[2],[-3]],[[1,2],[2],[-3]],[[2],[1],[-3]]],nchars=15,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,2,1,1],galrep=Int[1,2,3,4,5,6,7,9,13,14],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="S4",gens=[perm"(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)",perm"(1,9,5)(2,10,6)(3,11,7)(4,12,8)(13,17,21)(14,18,22)(15,19,23)(16,20,24)",perm"(1,2)(3,4)(5,8)(6,7)(9,11)(10,12)(13,15)(14,16)(17,18)(19,20)(21,24)(22,23)"],rels=Vector{Int}[[1,1],[3,3],[2,2,2],[-2,1,-2,1],[3,-2,3,-2,3,-2],[1,2,3,1,2,3]],nontrivrels=Vector{Int}[[-2,1,-2,1],[3,-2,3,-2,3,-2],[1,2,3,1,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,9),(3,8),(4,6)],ordersubdis=Tuple{Int,Int}[(1,1),(2,9),(3,4),(4,7),(6,4),(8,3),(12,1),(24,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"24",aut_gens=Vector{Vector{Int}}[[[1],[-2],[2,3,-2]],[[1,2],[2],[2,3,-2]],[[1,2,3,-2,3],[3,2],[3]]],nchars=5,dims=Int[1,1,2,3,3],schur=Int[1,1,1,1,1],galrep=Int[1,2,3,4,5],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*A4",gens=[perm"(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)",perm"(1,9,5)(2,10,6)(3,11,7)(4,12,8)(13,21,17)(14,22,18)(15,23,19)(16,24,20)",perm"(1,3)(2,4)(5,6)(7,8)(9,12)(10,11)(13,15)(14,16)(17,18)(19,20)(21,24)(22,23)"],rels=Vector{Int}[[1,1],[3,3],[2,2,2],[-2,1,2,1],[1,3,1,3],[3,-2,3,-2,3,-2]],nontrivrels=Vector{Int}[[-2,1,2,1],[1,3,1,3],[3,-2,3,-2,3,-2]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(3,8),(6,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(3,4),(4,7),(6,4),(8,1),(12,1),(24,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"24",aut_gens=Vector{Vector{Int}}[[[1],[2],[3,-2,3,2]],[[1],[3,2],[3]],[[1],[-2],[-2,3,2]]],nchars=8,dims=Int[1,1,1,1,1,1,3,3],schur=Int[1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,7,8],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2^2*S3",gens=[perm"(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)",perm"(1,7)(2,8)(3,9)(4,10)(5,11)(6,12)(13,19)(14,20)(15,21)(16,22)(17,23)(18,24)",perm"(1,4)(2,5)(3,6)(7,10)(8,11)(9,12)(13,16)(14,17)(15,18)(19,22)(20,23)(21,24)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,14,15)(16,17,18)(19,20,21)(22,23,24)"],rels=Vector{Int}[[1,1],[2,2],[3,3],[4,4,4],[1,2,1,2],[1,3,1,3],[2,3,2,3],[1,-4,1,-4],[2,-4,2,4],[3,-4,3,4]],nontrivrels=Vector{Int}[[1,2,1,2],[1,3,1,3],[2,3,2,3],[1,-4,1,-4],[2,-4,2,4],[3,-4,3,4]],orderdis=Tuple{Int,Int}[(1,1),(2,15),(3,2),(6,6)],ordersubdis=Tuple{Int,Int}[(1,1),(2,15),(3,1),(4,19),(6,7),(8,3),(12,7),(24,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"144",aut_gens=Vector{Vector{Int}}[[[1,4],[2],[3],[4]],[[1,3],[2],[3],[-4]],[[1],[3],[2],[-4]],[[1],[2,3],[3],[-4]]],nchars=12,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2^2*C6",gens=[perm"(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)",perm"(1,7)(2,8)(3,9)(4,10)(5,11)(6,12)(13,19)(14,20)(15,21)(16,22)(17,23)(18,24)",perm"(1,4)(2,5)(3,6)(7,10)(8,11)(9,12)(13,16)(14,17)(15,18)(19,22)(20,23)(21,24)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)"],rels=Vector{Int}[[1,1],[2,2],[3,3],[4,4,4],[1,2,1,2],[1,3,1,3],[2,3,2,3],[1,-4,1,4],[2,-4,2,4],[3,-4,3,4]],nontrivrels=Vector{Int}[[1,2,1,2],[1,3,1,3],[2,3,2,3],[1,-4,1,4],[2,-4,2,4],[3,-4,3,4]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(3,2),(6,14)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(3,1),(4,7),(6,7),(8,1),(12,7),(24,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"336",aut_gens=Vector{Vector{Int}}[[[1,2],[2],[3],[-4]],[[3],[1],[2],[-4]]],nchars=24,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="C25",gens=[perm"(1,25,20,15,10,5,24,19,14,9,4,23,18,13,8,3,22,17,12,7,2,21,16,11,6)"],rels=Vector{Int}[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[],orderdis=Tuple{Int,Int}[(1,1),(5,4),(25,20)],ordersubdis=Tuple{Int,Int}[(1,1),(5,1),(25,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"20",aut_gens=Vector{Vector{Int}}[[[1,1]]],nchars=25,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,6],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C5^2",gens=[perm"(1,21,16,11,6)(2,22,17,12,7)(3,23,18,13,8)(4,24,19,14,9)(5,25,20,15,10)",perm"(1,5,4,3,2)(6,10,9,8,7)(11,15,14,13,12)(16,20,19,18,17)(21,25,24,23,22)"],rels=Vector{Int}[[-1,-2,1,2],[1,1,1,1,1],[2,2,2,2,2]],nontrivrels=Vector{Int}[[-1,-2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(5,24)],ordersubdis=Tuple{Int,Int}[(1,1),(5,6),(25,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"480",aut_gens=Vector{Vector{Int}}[[[1,1],[2]],[[2,-1],[-1]]],nchars=25,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,6,7,8,9,10],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="D13",gens=[perm"(1,14)(2,15)(3,16)(4,17)(5,18)(6,19)(7,20)(8,21)(9,22)(10,23)(11,24)(12,25)(13,26)",perm"(1,13,12,11,10,9,8,7,6,5,4,3,2)(14,15,16,17,18,19,20,21,22,23,24,25,26)"],rels=Vector{Int}[[1,1],[-2,1,-2,1],[2,2,2,2,2,2,2,2,2,2,2,2,2]],nontrivrels=Vector{Int}[[-2,1,-2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,13),(13,12)],ordersubdis=Tuple{Int,Int}[(1,1),(2,13),(13,1),(26,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"156",aut_gens=Vector{Vector{Int}}[[[1,2,2,2,2],[2]],[[1],[-2,-2]]],nchars=8,dims=Int[1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1],galrep=Int[1,2,3],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C26",gens=[perm"(1,14)(2,15)(3,16)(4,17)(5,18)(6,19)(7,20)(8,21)(9,22)(10,23)(11,24)(12,25)(13,26)",perm"(1,13,12,11,10,9,8,7,6,5,4,3,2)(14,26,25,24,23,22,21,20,19,18,17,16,15)"],rels=Vector{Int}[[1,1],[-2,1,2,1],[2,2,2,2,2,2,2,2,2,2,2,2,2]],nontrivrels=Vector{Int}[[-2,1,2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(13,12),(26,12)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(13,1),(26,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"12",aut_gens=Vector{Vector{Int}}[[[1],[-2,-2,-2,-2,-2,-2]]],nchars=26,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="C27",gens=[perm"(1,27,18,9,24,15,6,21,12,3,26,17,8,23,14,5,20,11,2,25,16,7,22,13,4,19,10)"],rels=Vector{Int}[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[],orderdis=Tuple{Int,Int}[(1,1),(3,2),(9,6),(27,18)],ordersubdis=Tuple{Int,Int}[(1,1),(3,1),(9,1),(27,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"18",aut_gens=Vector{Vector{Int}}[[[1,1]]],nchars=27,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,4,10],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C3*C9",gens=[perm"(1,21,12,3,20,11,2,19,10)(4,24,15,6,23,14,5,22,13)(7,27,18,9,26,17,8,25,16)",perm"(1,7,4)(2,8,5)(3,9,6)(10,16,13)(11,17,14)(12,18,15)(19,25,22)(20,26,23)(21,27,24)"],rels=Vector{Int}[[2,2,2],[-1,-2,1,2],[1,1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[[-1,-2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(3,8),(9,18)],ordersubdis=Tuple{Int,Int}[(1,1),(3,4),(9,4),(27,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"108",aut_gens=Vector{Vector{Int}}[[[1],[2,-1,-1,-1,-1,-1,-1]],[[1,1],[2]],[[1,2],[-2]]],nchars=27,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,4,5,6,10,11,12],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="He3",gens=[perm"(1,19,10)(2,20,11)(3,21,12)(4,22,13)(5,23,14)(6,24,15)(7,25,16)(8,26,17)(9,27,18)",perm"(1,7,4)(2,8,5)(3,9,6)(10,18,14)(11,16,15)(12,17,13)(19,26,24)(20,27,22)(21,25,23)"],rels=Vector{Int}[[1,1,1],[2,2,2],[2,-1,2,-1,2,-1],[1,2,1,2,1,2]],nontrivrels=Vector{Int}[[2,-1,2,-1,2,-1],[1,2,1,2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(3,26)],ordersubdis=Tuple{Int,Int}[(1,1),(3,13),(9,4),(27,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"432",aut_gens=Vector{Vector{Int}}[[[1],[1,2,-1,-2,1,2,-1]],[[-1],[2]],[[-1,2],[-1]]],nchars=11,dims=Int[1,1,1,1,1,1,1,1,1,3,3],schur=Int[1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,6,10],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C9:C3",gens=[perm"(1,21,12,3,20,11,2,19,10)(4,24,15,6,23,14,5,22,13)(7,27,18,9,26,17,8,25,16)",perm"(1,7,4)(2,8,5)(3,9,6)(10,18,14)(11,16,15)(12,17,13)(19,26,24)(20,27,22)(21,25,23)"],rels=Vector{Int}[[2,2,2],[1,2,1,1,-2],[-2,-1,-1,-1,-1,2,1]],nontrivrels=Vector{Int}[[1,2,1,1,-2],[-2,-1,-1,-1,-1,2,1]],orderdis=Tuple{Int,Int}[(1,1),(3,8),(9,18)],ordersubdis=Tuple{Int,Int}[(1,1),(3,4),(9,4),(27,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"54",aut_gens=Vector{Vector{Int}}[[[1],[2,-1,-1,-1,-1,-1,-1]],[[1,1],[2]],[[1,-2],[2]]],nchars=11,dims=Int[1,1,1,1,1,1,1,1,1,3,3],schur=Int[1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,7,10],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C3^3",gens=[perm"(1,19,10)(2,20,11)(3,21,12)(4,22,13)(5,23,14)(6,24,15)(7,25,16)(8,26,17)(9,27,18)",perm"(1,7,4)(2,8,5)(3,9,6)(10,16,13)(11,17,14)(12,18,15)(19,25,22)(20,26,23)(21,27,24)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,27,26)"],rels=Vector{Int}[[1,1,1],[2,2,2],[3,3,3],[-1,-2,1,2],[-1,-3,1,3],[-2,-3,2,3]],nontrivrels=Vector{Int}[[-1,-2,1,2],[-1,-3,1,3],[-2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(3,26)],ordersubdis=Tuple{Int,Int}[(1,1),(3,13),(9,13),(27,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"11232",aut_gens=Vector{Vector{Int}}[[[3,-1],[-1],[-2]],[[1],[2],[-1,-3]]],nchars=27,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,4,5,6,10,11,12,13,14,15,16,17,18],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="C7:C4",gens=[perm"(1,22,8,15)(2,23,9,16)(3,24,10,17)(4,25,11,18)(5,26,12,19)(6,27,13,20)(7,28,14,21)",perm"(1,7,6,5,4,3,2)(8,14,13,12,11,10,9)(15,16,17,18,19,20,21)(22,23,24,25,26,27,28)"],rels=Vector{Int}[[1,1,1,1],[-1,-2,1,-2],[2,2,2,2,2,2,2]],nontrivrels=Vector{Int}[[-1,-2,1,-2]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(4,14),(7,6),(14,6)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(4,7),(7,1),(14,1),(28,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"84",aut_gens=Vector{Vector{Int}}[[[1,-2,-2,-2],[2]],[[1],[-2,-2]],[[-1],[-2]]],nchars=10,dims=Int[1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,2,1,2,2],galrep=Int[1,2,3,5,7],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C28",gens=[perm"(1,16,2,15)(3,18,4,17)(5,20,6,19)(7,22,8,21)(9,24,10,23)(11,26,12,25)(13,28,14,27)",perm"(1,13,11,9,7,5,3)(2,14,12,10,8,6,4)(15,27,25,23,21,19,17)(16,28,26,24,22,20,18)"],rels=Vector{Int}[[1,1,1,1],[-1,-2,1,2],[2,2,2,2,2,2,2]],nontrivrels=Vector{Int}[[-1,-2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(4,2),(7,6),(14,6),(28,12)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(4,1),(7,1),(14,1),(28,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"12",aut_gens=Vector{Vector{Int}}[[[1],[-2,-2]],[[-1],[-2]]],nchars=28,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,5,6,7],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="D14",gens=[perm"(1,15)(2,16)(3,17)(4,18)(5,19)(6,20)(7,21)(8,22)(9,23)(10,24)(11,25)(12,26)(13,27)(14,28)",perm"(1,8)(2,9)(3,10)(4,11)(5,12)(6,13)(7,14)(15,22)(16,23)(17,24)(18,25)(19,26)(20,27)(21,28)",perm"(1,7,6,5,4,3,2)(8,14,13,12,11,10,9)(15,16,17,18,19,20,21)(22,23,24,25,26,27,28)"],rels=Vector{Int}[[1,1],[2,2],[1,2,1,2],[1,-3,1,-3],[2,-3,2,3],[3,3,3,3,3,3,3]],nontrivrels=Vector{Int}[[1,2,1,2],[1,-3,1,-3],[2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,15),(7,6),(14,6)],ordersubdis=Tuple{Int,Int}[(1,1),(2,15),(4,7),(7,1),(14,3),(28,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"84",aut_gens=Vector{Vector{Int}}[[[1,-3,-3,-3],[2],[3]],[[1],[2],[3,3,3]],[[1,2],[2],[-3]]],nchars=10,dims=Int[1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,7],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*C14",gens=[perm"(1,15)(2,16)(3,17)(4,18)(5,19)(6,20)(7,21)(8,22)(9,23)(10,24)(11,25)(12,26)(13,27)(14,28)",perm"(1,8)(2,9)(3,10)(4,11)(5,12)(6,13)(7,14)(15,22)(16,23)(17,24)(18,25)(19,26)(20,27)(21,28)",perm"(1,7,6,5,4,3,2)(8,14,13,12,11,10,9)(15,21,20,19,18,17,16)(22,28,27,26,25,24,23)"],rels=Vector{Int}[[1,1],[2,2],[1,2,1,2],[1,-3,1,3],[2,-3,2,3],[3,3,3,3,3,3,3]],nontrivrels=Vector{Int}[[1,2,1,2],[1,-3,1,3],[2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(7,6),(14,18)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(4,1),(7,1),(14,3),(28,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"36",aut_gens=Vector{Vector{Int}}[[[1],[2],[-3,-3]],[[1,2],[2],[-3]],[[2],[1],[-3]]],nchars=28,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="C29",gens=[perm"(1,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2)"],rels=Vector{Int}[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[],orderdis=Tuple{Int,Int}[(1,1),(29,28)],ordersubdis=Tuple{Int,Int}[(1,1),(29,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"28",aut_gens=Vector{Vector{Int}}[[[1,1]]],nchars=29,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="C5*S3",gens=[perm"(1,16)(2,17)(3,18)(4,19)(5,20)(6,21)(7,22)(8,23)(9,24)(10,25)(11,26)(12,27)(13,28)(14,29)(15,30)",perm"(1,13,10,7,4)(2,14,11,8,5)(3,15,12,9,6)(16,28,25,22,19)(17,29,26,23,20)(18,30,27,24,21)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,17,18)(19,20,21)(22,23,24)(25,26,27)(28,29,30)"],rels=Vector{Int}[[1,1],[3,3,3],[-2,1,2,1],[-2,-3,2,3],[1,-3,1,-3],[2,2,2,2,2]],nontrivrels=Vector{Int}[[-2,1,2,1],[-2,-3,2,3],[1,-3,1,-3]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(3,2),(5,4),(10,12),(15,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(3,1),(5,1),(6,1),(10,3),(15,1),(30,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"24",aut_gens=Vector{Vector{Int}}[[[1],[2],[-3]],[[1,3],[2],[3]],[[1],[-2,-2],[-3]]],nchars=15,dims=Int[1,1,1,1,1,1,1,1,1,1,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,11,12],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C3*D5",gens=[perm"(1,16)(2,17)(3,18)(4,19)(5,20)(6,21)(7,22)(8,23)(9,24)(10,25)(11,26)(12,27)(13,28)(14,29)(15,30)",perm"(1,11,6)(2,12,7)(3,13,8)(4,14,9)(5,15,10)(16,26,21)(17,27,22)(18,28,23)(19,29,24)(20,30,25)",perm"(1,5,4,3,2)(6,10,9,8,7)(11,15,14,13,12)(16,17,18,19,20)(21,22,23,24,25)(26,27,28,29,30)"],rels=Vector{Int}[[1,1],[2,2,2],[-2,1,2,1],[-2,-3,2,3],[1,-3,1,-3],[3,3,3,3,3]],nontrivrels=Vector{Int}[[-2,1,2,1],[-2,-3,2,3],[1,-3,1,-3]],orderdis=Tuple{Int,Int}[(1,1),(2,5),(3,2),(5,4),(6,10),(15,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,5),(3,1),(5,1),(6,5),(10,1),(15,1),(30,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"40",aut_gens=Vector{Vector{Int}}[[[1,-3],[2],[3]],[[1],[2],[-3,-3]],[[1],[-2],[-3]]],nchars=12,dims=Int[1,1,1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,5,7,9],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="D15",gens=[perm"(1,16)(2,17)(3,18)(4,19)(5,20)(6,21)(7,22)(8,23)(9,24)(10,25)(11,26)(12,27)(13,28)(14,29)(15,30)",perm"(1,11,6)(2,12,7)(3,13,8)(4,14,9)(5,15,10)(16,21,26)(17,22,27)(18,23,28)(19,24,29)(20,25,30)",perm"(1,5,4,3,2)(6,10,9,8,7)(11,15,14,13,12)(16,17,18,19,20)(21,22,23,24,25)(26,27,28,29,30)"],rels=Vector{Int}[[1,1],[2,2,2],[-2,1,-2,1],[-2,-3,2,3],[1,-3,1,-3],[3,3,3,3,3]],nontrivrels=Vector{Int}[[-2,1,-2,1],[-2,-3,2,3],[1,-3,1,-3]],orderdis=Tuple{Int,Int}[(1,1),(2,15),(3,2),(5,4),(15,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,15),(3,1),(5,1),(6,5),(10,3),(15,1),(30,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"120",aut_gens=Vector{Vector{Int}}[[[1],[-2],[-3]],[[1,2],[2],[3]],[[1,3,3],[2],[3]],[[1],[2],[3,3]]],nchars=9,dims=Int[1,1,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,6],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C30",gens=[perm"(1,16)(2,17)(3,18)(4,19)(5,20)(6,21)(7,22)(8,23)(9,24)(10,25)(11,26)(12,27)(13,28)(14,29)(15,30)",perm"(1,11,6)(2,12,7)(3,13,8)(4,14,9)(5,15,10)(16,26,21)(17,27,22)(18,28,23)(19,29,24)(20,30,25)",perm"(1,5,4,3,2)(6,10,9,8,7)(11,15,14,13,12)(16,20,19,18,17)(21,25,24,23,22)(26,30,29,28,27)"],rels=Vector{Int}[[1,1],[2,2,2],[-2,1,2,1],[-2,-3,2,3],[1,-3,1,3],[3,3,3,3,3]],nontrivrels=Vector{Int}[[-2,1,2,1],[-2,-3,2,3],[1,-3,1,3]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(3,2),(5,4),(6,2),(10,4),(15,8),(30,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(3,1),(5,1),(6,1),(10,1),(15,1),(30,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"8",aut_gens=Vector{Vector{Int}}[[[1],[2],[3,3]],[[1],[-2],[-3]]],nchars=30,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,7,8,9,10],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="C31",gens=[perm"(1,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2)"],rels=Vector{Int}[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[],orderdis=Tuple{Int,Int}[(1,1),(31,30)],ordersubdis=Tuple{Int,Int}[(1,1),(31,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"30",aut_gens=Vector{Vector{Int}}[[[1,1,1]]],nchars=31,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="C32",gens=[perm"(1,32,16,24,8,28,12,20,4,30,14,22,6,26,10,18,2,31,15,23,7,27,11,19,3,29,13,21,5,25,9,17)"],rels=Vector{Int}[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[],orderdis=Tuple{Int,Int}[(1,1),(2,1),(4,2),(8,4),(16,8),(32,16)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(4,1),(8,1),(16,1),(32,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"16",aut_gens=Vector{Vector{Int}}[[[1,1,1,1,1]],[[1,1,1]]],nchars=32,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,5,9,17],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2.C4^2",gens=[perm"(1,19,3,17)(2,20,4,18)(5,23,7,21)(6,24,8,22)(9,27,11,25)(10,28,12,26)(13,31,15,29)(14,32,16,30)",perm"(1,10,2,9)(3,12,4,11)(5,14,6,13)(7,16,8,15)(17,30,18,29)(19,32,20,31)(21,26,22,25)(23,28,24,27)"],rels=Vector{Int}[[1,1,1,1],[2,2,2,2],[-1,-2,1,1,2,-1],[-2,1,2,2,-1,-2],[-1,2,1,-2,-1,2,1,-2]],nontrivrels=Vector{Int}[[-1,-2,1,1,2,-1],[-2,1,2,2,-1,-2],[-1,2,1,-2,-1,2,1,-2]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(4,24)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(4,19),(8,19),(16,3),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"384",aut_gens=Vector{Vector{Int}}[[[-1],[2]],[[1,2],[2]],[[2],[1]]],nchars=20,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1],galrep=Int[1,2,3,4,5,6,7,9,10,11,17,18,19,20],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C4*C8",gens=[perm"(1,22,6,18,2,21,5,17)(3,24,8,20,4,23,7,19)(9,30,14,26,10,29,13,25)(11,32,16,28,12,31,15,27)",perm"(1,11,3,9)(2,12,4,10)(5,15,7,13)(6,16,8,14)(17,27,19,25)(18,28,20,26)(21,31,23,29)(22,32,24,30)"],rels=Vector{Int}[[2,2,2,2],[-1,-2,1,2],[1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[[-1,-2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(4,12),(8,16)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(4,7),(8,7),(16,3),(32,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"128",aut_gens=Vector{Vector{Int}}[[[1,1,1],[2]],[[1],[2,1,1]],[[1,2],[2]]],nchars=32,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,5,6,7,8,9,10,11,12,17,18,19],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2.OD16",gens=[perm"(1,22,6,18,2,21,5,17)(3,24,8,20,4,23,7,19)(9,30,14,26,10,29,13,25)(11,32,16,28,12,31,15,27)",perm"(1,11,3,9)(2,12,4,10)(5,15,7,13)(6,16,8,14)(17,28,19,26)(18,27,20,25)(21,32,23,30)(22,31,24,29)"],rels=Vector{Int}[[2,2,2,2],[-1,2,2,1,-2,-2],[-1,-1,-1,2,-1,-2],[1,-2,1,2,1,1],[2,1,-2,-1,-2,1,2,-1]],nontrivrels=Vector{Int}[[-1,2,2,1,-2,-2],[-1,-1,-1,2,-1,-2],[1,-2,1,2,1,1],[2,1,-2,-1,-2,1,2,-1]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(4,12),(8,16)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(4,7),(8,7),(16,3),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"128",aut_gens=Vector{Vector{Int}}[[[1,1,1],[2]],[[1],[2,1,1]],[[1,2],[2]]],nchars=20,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,10,11,17,18],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2^2:C8",gens=[perm"(1,20,4,18,2,19,3,17)(5,24,8,22,6,23,7,21)(9,28,12,26,10,27,11,25)(13,32,16,30,14,31,15,29)",perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)(17,29)(18,30)(19,31)(20,32)(21,25)(22,26)(23,27)(24,28)"],rels=Vector{Int}[[2,2],[-1,2,1,1,2,-1],[1,2,-1,2,1,2,-1,2],[1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[[-1,2,1,1,2,-1],[1,2,-1,2,1,2,-1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(4,8),(8,16)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(4,11),(8,11),(16,3),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"64",aut_gens=Vector{Vector{Int}}[[[1],[2,1,2,-1,2]],[[1],[2,1,1,1,1]],[[1,1,1],[2]],[[1,2],[2]]],nchars=20,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,7,9,13,17,18,19],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2^2.D4",gens=[perm"(1,19,3,17)(2,20,4,18)(5,23,7,21)(6,24,8,22)(9,28,12,25)(10,27,11,26)(13,32,16,29)(14,31,15,30)",perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)(17,29)(18,30)(19,31)(20,32)(21,25)(22,26)(23,27)(24,28)"],rels=Vector{Int}[[2,2],[1,1,1,1],[-1,2,-1,2,-1,2,-1,2],[2,-1,2,1,2,-1,2,1],[1,2,-1,-1,2,-1,-1,2,-1,-1,2,1]],nontrivrels=Vector{Int}[[-1,2,-1,2,-1,2,-1,2],[2,-1,2,1,2,-1,2,1],[1,2,-1,-1,2,-1,-1,2,-1,-1,2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,11),(4,20)],ordersubdis=Tuple{Int,Int}[(1,1),(2,11),(4,23),(8,11),(16,3),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"64",aut_gens=Vector{Vector{Int}}[[[1],[2,-1,2,1,-2]],[[-1],[2]],[[1,2],[2]]],nchars=11,dims=Int[1,1,1,1,1,1,1,1,2,2,4],schur=Int[1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,9,10,11],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2^3.C4",gens=[perm"(1,20,4,18,2,19,3,17)(5,24,8,22,6,23,7,21)(9,27,11,26,10,28,12,25)(13,31,15,30,14,32,16,29)",perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)(17,29)(18,30)(19,31)(20,32)(21,25)(22,26)(23,27)(24,28)"],rels=Vector{Int}[[2,2],[2,1,1,2,1,1],[2,-1,2,1,2,-1,2,1],[1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[[2,1,1,2,1,1],[2,-1,2,1,2,-1,2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,11),(4,4),(8,16)],ordersubdis=Tuple{Int,Int}[(1,1),(2,11),(4,15),(8,11),(16,3),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"128",aut_gens=Vector{Vector{Int}}[[[1,1,1],[2]],[[1],[2,1,1]],[[1,2],[2]]],nchars=11,dims=Int[1,1,1,1,1,1,1,1,2,2,4],schur=Int[1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,9,10,11],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="OD16.C2",gens=[perm"(1,20,4,18,2,19,3,17)(5,24,8,22,6,23,7,21)(9,27,11,26,10,28,12,25)(13,31,15,30,14,32,16,29)",perm"(1,10,2,9)(3,12,4,11)(5,14,6,13)(7,16,8,15)(17,30,18,29)(19,32,20,31)(21,26,22,25)(23,28,24,27)"],rels=Vector{Int}[[2,2,2,2],[-2,-2,-1,-1,-1,-1],[-2,1,1,2,1,1],[2,1,2,1,2,-1,-2,-1]],nontrivrels=Vector{Int}[[-2,-2,-1,-1,-1,-1],[-2,1,1,2,1,1],[2,1,2,1,2,-1,-2,-1]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(4,12),(8,16)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(4,7),(8,11),(16,3),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"128",aut_gens=Vector{Vector{Int}}[[[1,1,1],[2]],[[1],[2,1,1]],[[1,2],[2]]],nchars=11,dims=Int[1,1,1,1,1,1,1,1,2,2,4],schur=Int[1,1,1,1,1,1,1,1,1,1,2],galrep=Int[1,2,3,4,5,6,9,10,11],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="D4:C4",gens=[perm"(1,19,3,17)(2,20,4,18)(5,23,7,21)(6,24,8,22)(9,27,11,25)(10,28,12,26)(13,31,15,29)(14,32,16,30)",perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)(17,29)(18,30)(19,31)(20,32)(21,26)(22,25)(23,28)(24,27)"],rels=Vector{Int}[[2,2],[1,1,1,1],[-1,2,1,1,2,-1],[2,-1,2,1,2,-1,2,1,2,-1,2,1,2,-1,2,1]],nontrivrels=Vector{Int}[[-1,2,1,1,2,-1],[2,-1,2,1,2,-1,2,1,2,-1,2,1,2,-1,2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,11),(4,12),(8,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,11),(4,19),(8,11),(16,3),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"64",aut_gens=Vector{Vector{Int}}[[[1],[2,1,1,2,-1,2,-1]],[[1,1,-2,1,-2,-1,-1],[2]],[[1,1,2,-1,2,1,2,-1,2],[2]],[[-1],[2]],[[1],[2,-1,-1]]],nchars=14,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,9,10,11,12],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="Q8:C4",gens=[perm"(1,19,3,17)(2,20,4,18)(5,23,7,21)(6,24,8,22)(9,27,11,25)(10,28,12,26)(13,31,15,29)(14,32,16,30)",perm"(1,10,2,9)(3,12,4,11)(5,14,6,13)(7,16,8,15)(17,30,18,29)(19,32,20,31)(21,25,22,26)(23,27,24,28)"],rels=Vector{Int}[[1,1,1,1],[2,2,2,2],[-1,-2,1,1,2,-1],[-2,1,2,2,-1,-2],[2,-1,2,1,2,1,-2,-1]],nontrivrels=Vector{Int}[[-1,-2,1,1,2,-1],[-2,1,2,2,-1,-2],[2,-1,2,1,2,1,-2,-1]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(4,20),(8,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(4,11),(8,11),(16,3),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"64",aut_gens=Vector{Vector{Int}}[[[1],[2,1,-2,-1,2,2,2]],[[1,-2,-2,-2,1,2,-1],[2]],[[1,-2,-2],[2]],[[-1],[2]],[[1],[2,-1,-1]]],nchars=14,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,2,2,1],galrep=Int[1,2,3,4,5,7,9,10,11,12],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C4wrC2",gens=[perm"(1,20,4,18,2,19,3,17)(5,24,8,22,6,23,7,21)(9,28,12,26,10,27,11,25)(13,32,16,30,14,31,15,29)",perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)(17,29)(18,30)(19,31)(20,32)(21,26)(22,25)(23,28)(24,27)"],rels=Vector{Int}[[2,2],[-1,2,1,1,2,-1],[2,-1,2,-1,2,-1,2,-1],[1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[[-1,2,1,1,2,-1],[2,-1,2,-1,2,-1,2,-1]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(4,16),(8,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(4,11),(8,11),(16,3),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"32",aut_gens=Vector{Vector{Int}}[[[1],[2,1,2,-1,2,1,1,1,1]],[[-1,-1,-1,-2,1,-2,-1],[2]],[[1,1,1,1,1],[2]],[[1,1,1],[2]]],nchars=14,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,9,10,11,13],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C4:C8",gens=[perm"(1,20,4,18,2,19,3,17)(5,24,8,22,6,23,7,21)(9,28,12,26,10,27,11,25)(13,32,16,30,14,31,15,29)",perm"(1,13,5,9)(2,14,6,10)(3,15,7,11)(4,16,8,12)(17,25,21,29)(18,26,22,30)(19,27,23,31)(20,28,24,32)"],rels=Vector{Int}[[2,2,2,2],[-1,-2,1,-2],[1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[[-1,-2,1,-2]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(4,12),(8,16)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(4,7),(8,7),(16,3),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"64",aut_gens=Vector{Vector{Int}}[[[1],[-2]],[[1],[2,1,1,1,1]],[[1,1,1],[2]],[[1,2],[2]]],nchars=20,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1],galrep=Int[1,2,3,4,5,6,9,11,17,18,19],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C8:C4",gens=[perm"(1,19,3,17)(2,20,4,18)(5,23,7,21)(6,24,8,22)(9,27,11,25)(10,28,12,26)(13,31,15,29)(14,32,16,30)",perm"(1,14,6,10,2,13,5,9)(3,16,8,12,4,15,7,11)(17,26,21,30,18,25,22,29)(19,28,23,32,20,27,24,31)"],rels=Vector{Int}[[1,1,1,1],[-2,-1,-1,2,-1,-1],[-2,1,2,2,2,-1],[-1,-1,-2,1,1,2]],nontrivrels=Vector{Int}[[-2,-1,-1,2,-1,-1],[-2,1,2,2,2,-1],[-1,-1,-2,1,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(4,20),(8,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(4,11),(8,7),(16,3),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"128",aut_gens=Vector{Vector{Int}}[[[1],[2,2,2]],[[1],[2,2,2,2,2]],[[1],[2,-1,-1]],[[1,2],[2]]],nchars=14,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,2,1,1,1,1],galrep=Int[1,2,3,4,5,6,9,10,11,12],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2.D8",gens=[perm"(1,19,3,17)(2,20,4,18)(5,23,7,21)(6,24,8,22)(9,27,11,25)(10,28,12,26)(13,31,15,29)(14,32,16,30)",perm"(1,13,5,10,2,14,6,9)(3,15,7,12,4,16,8,11)(17,25,22,30,18,26,21,29)(19,27,24,32,20,28,23,31)"],rels=Vector{Int}[[1,1,1,1],[-1,-2,1,-2],[2,2,2,2,2,2,2,2]],nontrivrels=Vector{Int}[[-1,-2,1,-2]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(4,20),(8,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(4,11),(8,7),(16,3),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"128",aut_gens=Vector{Vector{Int}}[[[1],[-2]],[[1],[-2,-2,-2]],[[1],[2,-1,-1]],[[1,2],[2]]],nchars=14,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,2,1,1,2,2],galrep=Int[1,2,3,4,5,6,9,10,11,13],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C8.C4",gens=[perm"(1,20,4,18,2,19,3,17)(5,24,8,22,6,23,7,21)(9,28,12,26,10,27,11,25)(13,32,16,30,14,31,15,29)",perm"(1,14,6,10,2,13,5,9)(3,16,8,12,4,15,7,11)(17,26,21,30,18,25,22,29)(19,28,23,32,20,27,24,31)"],rels=Vector{Int}[[2,2,1,2,2,-1],[-2,-2,-2,1,2,-1],[1,1,2,1,2,1]],nontrivrels=Vector{Int}[[2,2,1,2,2,-1],[-2,-2,-2,1,2,-1],[1,1,2,1,2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(4,4),(8,24)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(4,3),(8,7),(16,3),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"64",aut_gens=Vector{Vector{Int}}[[[1],[2,2,2]],[[1],[2,1,1,1,1]],[[1,1,1],[2]],[[1,2],[2]]],nchars=14,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,2,1,1,1,1],galrep=Int[1,2,3,4,5,6,9,10,11],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*C16",gens=[perm"(1,24,8,20,4,22,6,18,2,23,7,19,3,21,5,17)(9,32,16,28,12,30,14,26,10,31,15,27,11,29,13,25)",perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)(17,25)(18,26)(19,27)(20,28)(21,29)(22,30)(23,31)(24,32)"],rels=Vector{Int}[[2,2],[-1,2,1,2],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[[-1,2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(4,4),(8,8),(16,16)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(4,3),(8,3),(16,3),(32,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"32",aut_gens=Vector{Vector{Int}}[[[1],[2,-1,-1,-1,-1,-1,-1,-1,-1]],[[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[2]],[[1,1,1],[2]],[[1,2],[2]]],nchars=32,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,9,10,17,18],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="OD32",gens=[perm"(1,24,8,20,4,22,6,18,2,23,7,19,3,21,5,17)(9,32,16,28,12,30,14,26,10,31,15,27,11,29,13,25)",perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)(17,26)(18,25)(19,28)(20,27)(21,30)(22,29)(23,32)(24,31)"],rels=Vector{Int}[[2,2],[-1,-1,2,1,1,2],[2,-1,-1,-1,-1,-1,2,-1,-1,-1]],nontrivrels=Vector{Int}[[-1,-1,2,1,1,2],[2,-1,-1,-1,-1,-1,2,-1,-1,-1]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(4,4),(8,8),(16,16)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(4,3),(8,3),(16,3),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"32",aut_gens=Vector{Vector{Int}}[[[1],[2,-1,-1,-1,-1,-1,-1,-1,-1]],[[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[2]],[[1,1,1],[2]],[[1,2],[2]]],nchars=20,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,9,12,17],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="D16",gens=[perm"(1,17)(2,18)(3,19)(4,20)(5,21)(6,22)(7,23)(8,24)(9,25)(10,26)(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)",perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)(17,29)(18,30)(19,31)(20,32)(21,28)(22,27)(23,25)(24,26)"],rels=Vector{Int}[[1,1],[2,2],[1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2]],nontrivrels=Vector{Int}[[1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,17),(4,2),(8,4),(16,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,17),(4,9),(8,5),(16,3),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"128",aut_gens=Vector{Vector{Int}}[[[1],[2,1,1,2,1,2,1]],[[-2,-1,-2,-1,-1,-1,-2,-1,-2,-1,-1],[2]],[[2],[1]]],nchars=11,dims=Int[1,1,1,1,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,8],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="SD32",gens=[perm"(1,18,2,17)(3,20,4,19)(5,22,6,21)(7,24,8,23)(9,26,10,25)(11,28,12,27)(13,30,14,29)(15,32,16,31)",perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)(17,29)(18,30)(19,31)(20,32)(21,28)(22,27)(23,25)(24,26)"],rels=Vector{Int}[[2,2],[1,1,1,1],[-1,2,1,1,2,-1],[2,-1,2,-1,2,-1,2,1,2,-1,2,1,2,-1,2,1]],nontrivrels=Vector{Int}[[-1,2,1,1,2,-1],[2,-1,2,-1,2,-1,2,1,2,-1,2,1,2,-1,2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,9),(4,10),(8,4),(16,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,9),(4,9),(8,5),(16,3),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"64",aut_gens=Vector{Vector{Int}}[[[1],[2,1,1,2,-1,2,-1]],[[1,1,-2,1,-2,-1,-1],[2]],[[1,1,-2,1,-2,-1,-2,1,-2,-1,-1],[2]]],nchars=11,dims=Int[1,1,1,1,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,8],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="Q32",gens=[perm"(1,18,2,17)(3,20,4,19)(5,22,6,21)(7,24,8,23)(9,26,10,25)(11,28,12,27)(13,30,14,29)(15,32,16,31)",perm"(1,10,2,9)(3,12,4,11)(5,14,6,13)(7,16,8,15)(17,30,18,29)(19,32,20,31)(21,27,22,28)(23,26,24,25)"],rels=Vector{Int}[[-1,-1,-2,-2],[-1,-1,2,2],[-2,-1,2,1,2,1,2,1,2,-1,2,1,2,1,2,1]],nontrivrels=Vector{Int}[[-1,-1,-2,-2],[-1,-1,2,2],[-2,-1,2,1,2,1,2,1,2,-1,2,1,2,1,2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(4,18),(8,4),(16,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(4,9),(8,5),(16,3),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"128",aut_gens=Vector{Vector{Int}}[[[1],[-1,-2,-1]],[[1,1,2,1,2,1,2,1,2],[2]],[[2],[1]]],nchars=11,dims=Int[1,1,1,1,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,2,2,2,2],galrep=Int[1,2,3,4,5,6,8],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*C4^2",gens=[perm"(1,19,3,17)(2,20,4,18)(5,23,7,21)(6,24,8,22)(9,27,11,25)(10,28,12,26)(13,31,15,29)(14,32,16,30)",perm"(1,10,2,9)(3,12,4,11)(5,14,6,13)(7,16,8,15)(17,26,18,25)(19,28,20,27)(21,30,22,29)(23,32,24,31)",perm"(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,23)(20,24)(25,29)(26,30)(27,31)(28,32)"],rels=Vector{Int}[[3,3],[1,1,1,1],[2,2,2,2],[-1,-2,1,2],[-1,3,1,3],[-2,3,2,3]],nontrivrels=Vector{Int}[[-1,-2,1,2],[-1,3,1,3],[-2,3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(4,24)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(4,19),(8,19),(16,7),(32,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"1536",aut_gens=Vector{Vector{Int}}[[[1],[2],[3,-1,-1]],[[1,2],[2],[3]],[[1],[2,3],[3]],[[1],[1,2,3],[3]]],nchars=32,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,9,10,11,12,13,14,15,16,17,18,19,20,21,22],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*C2^2:C4",gens=[perm"(1,18,2,17)(3,20,4,19)(5,22,6,21)(7,24,8,23)(9,26,10,25)(11,28,12,27)(13,30,14,29)(15,32,16,31)",perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)(17,27)(18,28)(19,25)(20,26)(21,31)(22,32)(23,29)(24,30)",perm"(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,23)(20,24)(25,29)(26,30)(27,31)(28,32)"],rels=Vector{Int}[[2,2],[3,3],[1,1,1,1],[-1,3,1,3],[2,3,2,3],[-1,2,1,1,2,-1],[-1,2,1,2,-1,2,1,2]],nontrivrels=Vector{Int}[[-1,3,1,3],[2,3,2,3],[-1,2,1,1,2,-1],[-1,2,1,2,-1,2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,15),(4,16)],ordersubdis=Tuple{Int,Int}[(1,1),(2,15),(4,43),(8,27),(16,7),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"512",aut_gens=Vector{Vector{Int}}[[[1],[2],[3,-1,-1]],[[1],[2,3],[3]],[[1,2],[2],[3]]],nchars=20,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,17,18,19,20],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*C4:C4",gens=[perm"(1,18,2,17)(3,20,4,19)(5,22,6,21)(7,24,8,23)(9,26,10,25)(11,28,12,27)(13,30,14,29)(15,32,16,31)",perm"(1,11,3,9)(2,12,4,10)(5,15,7,13)(6,16,8,14)(17,25,19,27)(18,26,20,28)(21,29,23,31)(22,30,24,32)",perm"(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,23)(20,24)(25,29)(26,30)(27,31)(28,32)"],rels=Vector{Int}[[3,3],[2,2,2,2],[1,1,1,1],[-1,-2,1,-2],[-1,3,1,3],[-2,3,2,3]],nontrivrels=Vector{Int}[[-1,-2,1,-2],[-1,3,1,3],[-2,3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(4,24)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(4,19),(8,19),(16,7),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"512",aut_gens=Vector{Vector{Int}}[[[1],[2],[3,-2,-2]],[[1],[2],[3,-1,-1]],[[1],[2,3],[3]],[[1,2],[2],[3]]],nchars=20,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,17,18,19,20],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="(C2*C4):C4",gens=[perm"(1,18,2,17)(3,20,4,19)(5,22,6,21)(7,24,8,23)(9,26,10,25)(11,28,12,27)(13,30,14,29)(15,32,16,31)",perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)(17,27)(18,28)(19,25)(20,26)(21,31)(22,32)(23,29)(24,30)",perm"(1,7,3,5)(2,8,4,6)(9,15,11,13)(10,16,12,14)(17,23,19,21)(18,24,20,22)(25,31,27,29)(26,32,28,30)"],rels=Vector{Int}[[2,2],[3,3,3,3],[1,1,1,1],[-1,-3,1,3],[2,-3,2,3],[2,1,1,2,-1,-1],[1,2,3,-1,3,2]],nontrivrels=Vector{Int}[[-1,-3,1,3],[2,-3,2,3],[2,1,1,2,-1,-1],[1,2,3,-1,3,2]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(4,24)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(4,19),(8,11),(16,7),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"256",aut_gens=Vector{Vector{Int}}[[[1],[2,-1,-1],[3]],[[1],[2],[3,-1,-1]],[[1,3],[2],[3]],[[1,2],[2],[3]]],nchars=20,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,17,19],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C4*D4",gens=[perm"(1,18,2,17)(3,20,4,19)(5,22,6,21)(7,24,8,23)(9,26,10,25)(11,28,12,27)(13,30,14,29)(15,32,16,31)",perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)(17,27)(18,28)(19,25)(20,26)(21,31)(22,32)(23,29)(24,30)",perm"(1,6,2,5)(3,8,4,7)(9,14,10,13)(11,16,12,15)(17,22,18,21)(19,24,20,23)(25,30,26,29)(27,32,28,31)"],rels=Vector{Int}[[2,2],[3,1,1,3],[1,1,1,1],[-3,-1,-3,-1],[2,-3,2,3],[1,2,-1,2,1,2,-1,2]],nontrivrels=Vector{Int}[[3,1,1,3],[-3,-1,-3,-1],[2,-3,2,3],[1,2,-1,2,1,2,-1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,11),(4,20)],ordersubdis=Tuple{Int,Int}[(1,1),(2,11),(4,23),(8,19),(16,7),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"128",aut_gens=Vector{Vector{Int}}[[[1],[2,1,2,-1,2],[3]],[[1],[2],[3,1,2,-1,2]],[[-1],[2],[3]],[[1],[2],[-3]],[[2,3],[1,3],[3]]],nchars=20,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,17,18,19],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C4*Q8",gens=[perm"(1,18,2,17)(3,20,4,19)(5,22,6,21)(7,24,8,23)(9,26,10,25)(11,28,12,27)(13,30,14,29)(15,32,16,31)",perm"(1,11,3,9)(2,12,4,10)(5,15,7,13)(6,16,8,14)(17,25,19,27)(18,26,20,28)(21,29,23,31)(22,30,24,32)",perm"(1,8,4,5)(2,7,3,6)(9,16,12,13)(10,15,11,14)(17,24,20,21)(18,23,19,22)(25,32,28,29)(26,31,27,30)"],rels=Vector{Int}[[2,2,2,2],[1,1,1,1],[3,3,3,3],[-1,-2,1,-2],[-1,-3,1,3],[-2,-3,2,3],[2,2,-3,-3,1,1]],nontrivrels=Vector{Int}[[-1,-2,1,-2],[-1,-3,1,3],[-2,-3,2,3],[2,2,-3,-3,1,1]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(4,28)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(4,15),(8,11),(16,7),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"384",aut_gens=Vector{Vector{Int}}[[[1],[2],[3,-2,-2]],[[1],[2],[3,-1,-1]],[[1,2],[2],[3]],[[2,3],[1,3],[3]]],nchars=20,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,17,18,19],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2^2wrC2",gens=[perm"(1,17)(2,18)(3,19)(4,20)(5,21)(6,22)(7,23)(8,24)(9,25)(10,26)(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)",perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)(17,27)(18,28)(19,25)(20,26)(21,31)(22,32)(23,29)(24,30)",perm"(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,22)(18,21)(19,24)(20,23)(25,30)(26,29)(27,32)(28,31)"],rels=Vector{Int}[[1,1],[2,2],[3,3],[2,3,2,3],[2,1,3,1,2,1,3,1],[1,2,1,2,1,2,1,2],[1,3,1,3,1,3,1,3],[3,1,3,2,1,3,2,1,3,2,1,2]],nontrivrels=Vector{Int}[[2,3,2,3],[2,1,3,1,2,1,3,1],[1,2,1,2,1,2,1,2],[1,3,1,3,1,3,1,3],[3,1,3,2,1,3,2,1,3,2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,19),(4,12)],ordersubdis=Tuple{Int,Int}[(1,1),(2,19),(4,47),(8,31),(16,7),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"384",aut_gens=Vector{Vector{Int}}[[[1,1,2,1,2],[2],[3]],[[1],[2,1,2,1,2],[3]],[[1],[2,3],[3]],[[1],[2],[2,3]]],nchars=14,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,13,14],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2^2:D4",gens=[perm"(1,17)(2,18)(3,19)(4,20)(5,21)(6,22)(7,23)(8,24)(9,25)(10,26)(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)",perm"(1,11,3,9)(2,12,4,10)(5,15,7,13)(6,16,8,14)(17,25,19,27)(18,26,20,28)(21,29,23,31)(22,30,24,32)",perm"(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,22)(18,21)(19,24)(20,23)(25,30)(26,29)(27,32)(28,31)"],rels=Vector{Int}[[1,1],[3,3],[2,2,2,2],[-2,1,-2,1],[-2,3,2,3],[1,3,1,3,1,3,1,3]],nontrivrels=Vector{Int}[[-2,1,-2,1],[-2,3,2,3],[1,3,1,3,1,3,1,3]],orderdis=Tuple{Int,Int}[(1,1),(2,15),(4,16)],ordersubdis=Tuple{Int,Int}[(1,1),(2,15),(4,27),(8,23),(16,7),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"128",aut_gens=Vector{Vector{Int}}[[[1],[-2],[3,1,3,1,3]],[[1],[-2],[3]],[[1],[2,1,3,1,3],[3]],[[1],[2],[3,-2,-2]],[[1,2],[2],[3]]],nchars=14,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,13],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2^2:Q8",gens=[perm"(1,19,3,17)(2,20,4,18)(5,23,7,21)(6,24,8,22)(9,27,11,25)(10,28,12,26)(13,31,15,29)(14,32,16,30)",perm"(1,11,3,9)(2,12,4,10)(5,15,7,13)(6,16,8,14)(17,25,19,27)(18,26,20,28)(21,29,23,31)(22,30,24,32)",perm"(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,22)(18,21)(19,24)(20,23)(25,30)(26,29)(27,32)(28,31)"],rels=Vector{Int}[[3,3],[-1,-1,2,2],[-1,-2,1,-2],[2,2,-1,-1],[-2,3,2,3],[1,3,-1,3,1,3,-1,3]],nontrivrels=Vector{Int}[[-1,-1,2,2],[-1,-2,1,-2],[2,2,-1,-1],[-2,3,2,3],[1,3,-1,3,1,3,-1,3]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(4,24)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(4,19),(8,15),(16,7),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"128",aut_gens=Vector{Vector{Int}}[[[1],[-2],[3,1,3,-1,3]],[[1],[-2],[3]],[[1],[2,1,3,-1,3],[3]],[[1],[2],[3,-1,-1]],[[1,2],[2],[3]]],nchars=14,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,2,2,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,13],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="(C2^2*C4):C2",gens=[perm"(1,17)(2,18)(3,19)(4,20)(5,21)(6,22)(7,23)(8,24)(9,25)(10,26)(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)",perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)(17,27)(18,28)(19,25)(20,26)(21,31)(22,32)(23,29)(24,30)",perm"(1,7,3,5)(2,8,4,6)(9,15,11,13)(10,16,12,14)(17,24,19,22)(18,23,20,21)(25,32,27,30)(26,31,28,29)"],rels=Vector{Int}[[1,1],[2,2],[2,3,2,-3],[3,3,3,3],[1,3,3,1,3,3],[-3,1,2,1,-3,2],[1,-3,1,3,1,-3,1,3]],nontrivrels=Vector{Int}[[2,3,2,-3],[1,3,3,1,3,3],[-3,1,2,1,-3,2],[1,-3,1,3,1,-3,1,3]],orderdis=Tuple{Int,Int}[(1,1),(2,11),(4,20)],ordersubdis=Tuple{Int,Int}[(1,1),(2,11),(4,23),(8,15),(16,7),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"128",aut_gens=Vector{Vector{Int}}[[[1,1,-3,1,3],[2],[3]],[[1],[2,-3,-3],[3]],[[1],[2,1,-3,1,3],[3]],[[1],[2],[2,3]]],nchars=14,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,13],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C4.D4",gens=[perm"(1,17)(2,18)(3,19)(4,20)(5,21)(6,22)(7,23)(8,24)(9,25)(10,26)(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)",perm"(1,10,2,9)(3,12,4,11)(5,14,6,13)(7,16,8,15)(17,28,18,27)(19,26,20,25)(21,32,22,31)(23,30,24,29)",perm"(1,7,3,5)(2,8,4,6)(9,15,11,13)(10,16,12,14)(17,24,19,22)(18,23,20,21)(25,32,27,30)(26,31,28,29)"],rels=Vector{Int}[[1,1],[3,3,3,3],[2,2,2,2],[-2,-3,2,3],[1,3,3,1,-3,-3],[1,2,2,1,-2,-2],[-2,1,-3,1,-2,3],[3,3,-2,1,2,1]],nontrivrels=Vector{Int}[[-2,-3,2,3],[1,3,3,1,-3,-3],[1,2,2,1,-2,-2],[-2,1,-3,1,-2,3],[3,3,-2,1,2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,11),(4,20)],ordersubdis=Tuple{Int,Int}[(1,1),(2,11),(4,23),(8,15),(16,7),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"256",aut_gens=Vector{Vector{Int}}[[[1],[2,-3,-3],[3]],[[1],[-2],[3]],[[1,2,3],[2],[3]],[[1,2,3],[3],[2]]],nchars=14,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,13],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C4.Q8",gens=[perm"(1,19,3,17)(2,20,4,18)(5,23,7,21)(6,24,8,22)(9,27,11,25)(10,28,12,26)(13,31,15,29)(14,32,16,30)",perm"(1,10,2,9)(3,12,4,11)(5,14,6,13)(7,16,8,15)(17,28,18,27)(19,26,20,25)(21,32,22,31)(23,30,24,29)",perm"(1,7,3,5)(2,8,4,6)(9,15,11,13)(10,16,12,14)(17,24,19,22)(18,23,20,21)(25,32,27,30)(26,31,28,29)"],rels=Vector{Int}[[-1,-1,-3,-3],[-1,-1,3,3],[2,2,2,2],[-1,-2,-1,2],[-2,-3,2,3],[-1,-3,1,3,2,2]],nontrivrels=Vector{Int}[[-1,-1,-3,-3],[-1,-1,3,3],[-1,-2,-1,2],[-2,-3,2,3],[-1,-3,1,3,2,2]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(4,28)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(4,15),(8,7),(16,7),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"256",aut_gens=Vector{Vector{Int}}[[[1],[2,-1,-1],[3]],[[1],[-2],[3]],[[1,3],[3],[2]]],nchars=14,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,2,2,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C4^2:C2",gens=[perm"(1,17)(2,18)(3,19)(4,20)(5,21)(6,22)(7,23)(8,24)(9,25)(10,26)(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)",perm"(1,12,4,9)(2,11,3,10)(5,16,8,13)(6,15,7,14)(17,26,20,27)(18,25,19,28)(21,30,24,31)(22,29,23,32)",perm"(1,7,3,5)(2,8,4,6)(9,15,11,13)(10,16,12,14)(17,24,19,22)(18,23,20,21)(25,32,27,30)(26,31,28,29)"],rels=Vector{Int}[[1,1],[3,3,3,3],[2,2,2,2],[-2,-3,2,3],[2,1,2,2,1,2],[1,3,3,1,-3,-3],[-2,1,2,1,-3,-3],[-2,1,-3,1,-3,-2]],nontrivrels=Vector{Int}[[-2,-3,2,3],[2,1,2,2,1,2],[1,3,3,1,-3,-3],[-2,1,2,1,-3,-3],[-2,1,-3,1,-3,-2]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(4,24)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(4,19),(8,7),(16,7),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"192",aut_gens=Vector{Vector{Int}}[[[1,-3,-3],[2],[3]],[[1],[-2,-3,-3],[3]],[[1],[2,3],[2]]],nchars=14,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,11,12],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C4:D4",gens=[perm"(1,17)(2,18)(3,19)(4,20)(5,21)(6,22)(7,23)(8,24)(9,25)(10,26)(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)",perm"(1,11,3,9)(2,12,4,10)(5,15,7,13)(6,16,8,14)(17,25,19,27)(18,26,20,28)(21,29,23,31)(22,30,24,32)",perm"(1,6,2,5)(3,8,4,7)(9,14,10,13)(11,16,12,15)(17,21,18,22)(19,23,20,24)(25,29,26,30)(27,31,28,32)"],rels=Vector{Int}[[1,1],[2,2,2,2],[3,3,3,3],[-2,1,-2,1],[-2,-3,2,3],[1,-3,1,-3]],nontrivrels=Vector{Int}[[-2,1,-2,1],[-2,-3,2,3],[1,-3,1,-3]],orderdis=Tuple{Int,Int}[(1,1),(2,19),(4,12)],ordersubdis=Tuple{Int,Int}[(1,1),(2,19),(4,31),(8,31),(16,7),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"1536",aut_gens=Vector{Vector{Int}}[[[1],[-2],[3]],[[1,2],[2],[3]],[[1],[2,3],[3]],[[1,2],[2],[2,3]]],nchars=14,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,13,14],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C4:Q8",gens=[perm"(1,19,3,17)(2,20,4,18)(5,23,7,21)(6,24,8,22)(9,27,11,25)(10,28,12,26)(13,31,15,29)(14,32,16,30)",perm"(1,11,3,9)(2,12,4,10)(5,15,7,13)(6,16,8,14)(17,25,19,27)(18,26,20,28)(21,29,23,31)(22,30,24,32)",perm"(1,6,2,5)(3,8,4,7)(9,14,10,13)(11,16,12,15)(17,21,18,22)(19,23,20,24)(25,29,26,30)(27,31,28,32)"],rels=Vector{Int}[[-1,-1,-2,-2],[-1,-2,1,-2],[-1,-1,2,2],[3,3,3,3],[-1,-3,1,-3],[-2,-3,2,3]],nontrivrels=Vector{Int}[[-1,-1,-2,-2],[-1,-2,1,-2],[-1,-1,2,2],[-1,-3,1,-3],[-2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(4,28)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(4,15),(8,15),(16,7),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"512",aut_gens=Vector{Vector{Int}}[[[1],[-2],[3]],[[1],[2,-3,-3],[3]],[[1,2,3],[2],[3]],[[1,2],[2],[2,3]]],nchars=14,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,2,1,2,2,2,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,13,14],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2^2*C8",gens=[perm"(1,20,4,18,2,19,3,17)(5,24,8,22,6,23,7,21)(9,28,12,26,10,27,11,25)(13,32,16,30,14,31,15,29)",perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)(17,25)(18,26)(19,27)(20,28)(21,29)(22,30)(23,31)(24,32)",perm"(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,23)(20,24)(25,29)(26,30)(27,31)(28,32)"],rels=Vector{Int}[[2,2],[3,3],[-1,2,1,2],[-1,3,1,3],[2,3,2,3],[1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[[-1,2,1,2],[-1,3,1,3],[2,3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(4,8),(8,16)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(4,11),(8,11),(16,7),(32,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"384",aut_gens=Vector{Vector{Int}}[[[1],[2],[3,1,1,1,1]],[[1,1,1],[2],[3]],[[1,2],[2],[3]],[[1],[2,3],[3]],[[1,2],[2],[2,3]]],nchars=32,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,17,18,19,20],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*OD16",gens=[perm"(1,20,4,18,2,19,3,17)(5,24,8,22,6,23,7,21)(9,28,12,26,10,27,11,25)(13,32,16,30,14,31,15,29)",perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)(17,26)(18,25)(19,28)(20,27)(21,30)(22,29)(23,32)(24,31)",perm"(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,23)(20,24)(25,29)(26,30)(27,31)(28,32)"],rels=Vector{Int}[[2,2],[3,3],[-1,3,1,3],[2,3,2,3],[-1,-1,-1,2,-1,2],[1,2,1,2,1,1],[-1,-1,-1,-1,2,1,2,-1]],nontrivrels=Vector{Int}[[-1,3,1,3],[2,3,2,3],[-1,-1,-1,2,-1,2],[1,2,1,2,1,1],[-1,-1,-1,-1,2,1,2,-1]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(4,8),(8,16)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(4,11),(8,11),(16,7),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"128",aut_gens=Vector{Vector{Int}}[[[1],[2],[3,1,1,1,1]],[[1,1,1],[2],[3]],[[1],[2,3],[3]],[[1,2],[2],[3]]],nchars=20,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,13,14,17,19],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="OD16:C2",gens=[perm"(1,20,4,18,2,19,3,17)(5,24,8,22,6,23,7,21)(9,28,12,26,10,27,11,25)(13,32,16,30,14,31,15,29)",perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)(17,25)(18,26)(19,27)(20,28)(21,29)(22,30)(23,31)(24,32)",perm"(1,5)(2,6)(3,7)(4,8)(9,14)(10,13)(11,16)(12,15)(17,21)(18,22)(19,23)(20,24)(25,30)(26,29)(27,32)(28,31)"],rels=Vector{Int}[[2,2],[3,3],[-1,2,1,2],[-1,3,1,3],[2,3,1,1,1,1,2,3],[3,2,3,2,3,2,3,2]],nontrivrels=Vector{Int}[[-1,2,1,2],[-1,3,1,3],[2,3,1,1,1,1,2,3],[3,2,3,2,3,2,3,2]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(4,8),(8,16)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(4,7),(8,11),(16,7),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"96",aut_gens=Vector{Vector{Int}}[[[1,1,1,1,1],[2],[3]],[[1,1,1],[2],[3]],[[1],[3],[2]],[[1],[2,3,1,1],[3]]],nchars=20,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,17],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*D8",gens=[perm"(1,17)(2,18)(3,19)(4,20)(5,21)(6,22)(7,23)(8,24)(9,25)(10,26)(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)",perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)(17,27)(18,28)(19,26)(20,25)(21,31)(22,32)(23,30)(24,29)",perm"(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,23)(20,24)(25,29)(26,30)(27,31)(28,32)"],rels=Vector{Int}[[1,1],[2,2],[3,3],[1,3,1,3],[2,3,2,3],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1]],nontrivrels=Vector{Int}[[1,3,1,3],[2,3,2,3],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,19),(4,4),(8,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,19),(4,27),(8,15),(16,7),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"256",aut_gens=Vector{Vector{Int}}[[[1],[2,1,1,2,1,2,1],[3]],[[1],[2],[3,1,2,1,2,1,2,1,2]],[[1,3],[2],[3]],[[2],[1],[3]]],nchars=14,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,13],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*SD16",gens=[perm"(1,18,2,17)(3,20,4,19)(5,22,6,21)(7,24,8,23)(9,26,10,25)(11,28,12,27)(13,30,14,29)(15,32,16,31)",perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)(17,27)(18,28)(19,26)(20,25)(21,31)(22,32)(23,30)(24,29)",perm"(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,23)(20,24)(25,29)(26,30)(27,31)(28,32)"],rels=Vector{Int}[[2,2],[3,3],[-1,3,1,3],[2,3,2,3],[1,2,1,1,2,1],[1,2,1,2,-1,2,1,2]],nontrivrels=Vector{Int}[[-1,3,1,3],[2,3,2,3],[1,2,1,1,2,1],[1,2,1,2,-1,2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,11),(4,12),(8,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,11),(4,19),(8,15),(16,7),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"128",aut_gens=Vector{Vector{Int}}[[[1],[2,-1,2,-1,2],[3]],[[1,-2,1,-2,1],[2],[3]],[[1],[2],[3,-1,-1]],[[1,3],[2],[3]],[[1],[2,3],[3]]],nchars=14,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*Q16",gens=[perm"(1,18,2,17)(3,20,4,19)(5,22,6,21)(7,24,8,23)(9,26,10,25)(11,28,12,27)(13,30,14,29)(15,32,16,31)",perm"(1,10,2,9)(3,12,4,11)(5,14,6,13)(7,16,8,15)(17,28,18,27)(19,25,20,26)(21,32,22,31)(23,29,24,30)",perm"(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,23)(20,24)(25,29)(26,30)(27,31)(28,32)"],rels=Vector{Int}[[3,3],[-1,-1,2,2],[1,1,1,1],[1,1,1,1],[-1,3,1,3],[-2,3,2,3],[2,-1,-2,1,-2,1,-2,-1]],nontrivrels=Vector{Int}[[-1,-1,2,2],[-1,3,1,3],[-2,3,2,3],[2,-1,-2,1,-2,1,-2,-1]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(4,20),(8,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(4,11),(8,15),(16,7),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"256",aut_gens=Vector{Vector{Int}}[[[1],[2,-1,-2,-1,2],[3]],[[1],[2],[3,-1,-1]],[[1,3],[2],[3]],[[2],[1],[3]]],nchars=14,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,2,2,2,2],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,13],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="D8:C2",gens=[perm"(1,17)(2,18)(3,19)(4,20)(5,21)(6,22)(7,23)(8,24)(9,25)(10,26)(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)",perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)(17,27)(18,28)(19,26)(20,25)(21,31)(22,32)(23,30)(24,29)",perm"(1,6,2,5)(3,8,4,7)(9,14,10,13)(11,16,12,15)(17,22,18,21)(19,24,20,23)(25,30,26,29)(27,32,28,31)"],rels=Vector{Int}[[1,1],[2,2],[3,3,3,3],[1,-3,1,3],[2,-3,2,3],[-3,-3,2,1,2,1,2,1,2,1]],nontrivrels=Vector{Int}[[1,-3,1,3],[2,-3,2,3],[-3,-3,2,1,2,1,2,1,2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,11),(4,12),(8,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,11),(4,11),(8,15),(16,7),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"64",aut_gens=Vector{Vector{Int}}[[[1],[2,1,2,1,2,-3,-3],[3]],[[1,-3,-3],[2],[3]],[[1],[2],[-3]],[[2],[1],[3]]],nchars=14,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C8:C2^2",gens=[perm"(1,17)(2,18)(3,19)(4,20)(5,21)(6,22)(7,23)(8,24)(9,25)(10,26)(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)",perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)(17,27)(18,28)(19,26)(20,25)(21,31)(22,32)(23,30)(24,29)",perm"(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,22)(18,21)(19,24)(20,23)(25,30)(26,29)(27,32)(28,31)"],rels=Vector{Int}[[1,1],[2,2],[3,3],[2,3,2,3],[1,2,1,3,1,2,1,3],[3,2,1,2,1,2,1,3,2,1]],nontrivrels=Vector{Int}[[2,3,2,3],[1,2,1,3,1,2,1,3],[3,2,1,2,1,2,1,3,2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,15),(4,8),(8,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,15),(4,19),(8,15),(16,7),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"64",aut_gens=Vector{Vector{Int}}[[[1],[2,1,1,2,1,2,1],[3,1,2,1,2,1,2,1,2]],[[-2,-1,-2,-1,-1],[2],[3]],[[1],[2],[3,1,2,1,2,1,2,1,2]],[[1],[2,3],[3]]],nchars=11,dims=Int[1,1,1,1,1,1,1,1,2,2,4],schur=Int[1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="SD16:C2",gens=[perm"(1,17)(2,18)(3,19)(4,20)(5,21)(6,22)(7,23)(8,24)(9,25)(10,26)(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)",perm"(1,10,2,9)(3,12,4,11)(5,14,6,13)(7,16,8,15)(17,28,18,27)(19,25,20,26)(21,32,22,31)(23,29,24,30)",perm"(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,22)(18,21)(19,24)(20,23)(25,30)(26,29)(27,32)(28,31)"],rels=Vector{Int}[[1,1],[3,3],[-2,3,2,3],[3,1,-2,-2,3,1],[1,-2,1,-2,1,-2,1,2]],nontrivrels=Vector{Int}[[-2,3,2,3],[3,1,-2,-2,3,1],[1,-2,1,-2,1,-2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(4,16),(8,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(4,11),(8,15),(16,7),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"64",aut_gens=Vector{Vector{Int}}[[[1],[1,-2,1,2,2],[3,-2,-2]],[[1,-2,-2,-1,2,-1,2],[2],[3]],[[1],[2],[3,-2,-2]],[[1],[2,3],[3]]],nchars=11,dims=Int[1,1,1,1,1,1,1,1,2,2,4],schur=Int[1,1,1,1,1,1,1,1,1,1,2],galrep=Int[1,2,3,4,5,6,7,8,9,10,11],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2^3*C4",gens=[perm"(1,18,2,17)(3,20,4,19)(5,22,6,21)(7,24,8,23)(9,26,10,25)(11,28,12,27)(13,30,14,29)(15,32,16,31)",perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)(17,25)(18,26)(19,27)(20,28)(21,29)(22,30)(23,31)(24,32)",perm"(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,23)(20,24)(25,29)(26,30)(27,31)(28,32)",perm"(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24)(25,27)(26,28)(29,31)(30,32)"],rels=Vector{Int}[[2,2],[3,3],[4,4],[1,1,1,1],[-1,2,1,2],[-1,3,1,3],[2,3,2,3],[-1,4,1,4],[2,4,2,4],[3,4,3,4]],nontrivrels=Vector{Int}[[-1,2,1,2],[-1,3,1,3],[2,3,2,3],[-1,4,1,4],[2,4,2,4],[3,4,3,4]],orderdis=Tuple{Int,Int}[(1,1),(2,15),(4,16)],ordersubdis=Tuple{Int,Int}[(1,1),(2,15),(4,43),(8,43),(16,15),(32,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"21504",aut_gens=Vector{Vector{Int}}[[[1],[2],[3],[4,-1,-1]],[[1,2],[2],[3],[4]],[[1],[2],[3],[2,4]],[[1],[2],[4],[2,3,4]],[[1],[3],[4],[2,3,4]]],nchars=32,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2^2*D4",gens=[perm"(1,17)(2,18)(3,19)(4,20)(5,21)(6,22)(7,23)(8,24)(9,25)(10,26)(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)",perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)(17,26)(18,25)(19,28)(20,27)(21,30)(22,29)(23,32)(24,31)",perm"(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,23)(20,24)(25,29)(26,30)(27,31)(28,32)",perm"(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24)(25,27)(26,28)(29,31)(30,32)"],rels=Vector{Int}[[1,1],[2,2],[3,3],[4,4],[2,4,2,4],[1,3,1,3],[2,3,2,3],[1,4,1,4],[3,4,3,4],[1,2,1,2,1,2,1,2]],nontrivrels=Vector{Int}[[2,4,2,4],[1,3,1,3],[2,3,2,3],[1,4,1,4],[3,4,3,4],[1,2,1,2,1,2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,23),(4,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,23),(4,67),(8,51),(16,15),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"3072",aut_gens=Vector{Vector{Int}}[[[1],[2],[3,1,2,1,2],[4]],[[1,4],[2],[3],[4]],[[1],[2],[4],[3]],[[1],[2],[3,4],[4]],[[2],[1],[3],[4]]],nchars=20,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2^2*Q8",gens=[perm"(1,18,2,17)(3,20,4,19)(5,22,6,21)(7,24,8,23)(9,26,10,25)(11,28,12,27)(13,30,14,29)(15,32,16,31)",perm"(1,10,2,9)(3,12,4,11)(5,14,6,13)(7,16,8,15)(17,25,18,26)(19,27,20,28)(21,29,22,30)(23,31,24,32)",perm"(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,23)(20,24)(25,29)(26,30)(27,31)(28,32)",perm"(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24)(25,27)(26,28)(29,31)(30,32)"],rels=Vector{Int}[[3,3],[4,4],[-1,-1,-2,-2],[-1,-2,1,-2],[-1,-1,2,2],[-1,3,1,3],[-2,3,2,3],[-1,4,1,4],[-2,4,2,4],[3,4,3,4]],nontrivrels=Vector{Int}[[-1,-1,-2,-2],[-1,-2,1,-2],[-1,-1,2,2],[-1,3,1,3],[-2,3,2,3],[-1,4,1,4],[-2,4,2,4],[3,4,3,4]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(4,24)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(4,19),(8,35),(16,15),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"9216",aut_gens=Vector{Vector{Int}}[[[1],[2],[3,-1,-1],[4]],[[1,4],[2],[3],[4]],[[1],[2],[4],[3]],[[1],[2],[3,4],[4]],[[1,2],[2],[3],[4]],[[2],[1],[3],[4]]],nchars=20,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*D4:C2",gens=[perm"(1,17)(2,18)(3,19)(4,20)(5,21)(6,22)(7,23)(8,24)(9,25)(10,26)(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)",perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)(17,26)(18,25)(19,28)(20,27)(21,30)(22,29)(23,32)(24,31)",perm"(1,6,2,5)(3,8,4,7)(9,14,10,13)(11,16,12,15)(17,22,18,21)(19,24,20,23)(25,30,26,29)(27,32,28,31)",perm"(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24)(25,27)(26,28)(29,31)(30,32)"],rels=Vector{Int}[[1,1],[2,2],[4,4],[3,3,3,3],[1,-3,1,3],[2,-3,2,3],[1,4,1,4],[2,4,2,4],[-3,4,3,4],[1,2,3,3,1,2]],nontrivrels=Vector{Int}[[1,-3,1,3],[2,-3,2,3],[1,4,1,4],[2,4,2,4],[-3,4,3,4],[1,2,3,3,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,15),(4,16)],ordersubdis=Tuple{Int,Int}[(1,1),(2,15),(4,27),(8,35),(16,15),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"768",aut_gens=Vector{Vector{Int}}[[[1],[2],[3],[4,-3,-3]],[[1],[2],[3,4],[4]],[[2],[1],[3],[4]],[[1,2,3],[2],[3],[4]]],nchars=20,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="Q8:C2^2",gens=[perm"(1,17)(2,18)(3,19)(4,20)(5,21)(6,22)(7,23)(8,24)(9,25)(10,26)(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)",perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)(17,26)(18,25)(19,28)(20,27)(21,30)(22,29)(23,32)(24,31)",perm"(1,5)(2,6)(3,7)(4,8)(9,14)(10,13)(11,16)(12,15)(17,21)(18,22)(19,23)(20,24)(25,30)(26,29)(27,32)(28,31)",perm"(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16)(17,20)(18,19)(21,24)(22,23)(25,28)(26,27)(29,32)(30,31)"],rels=Vector{Int}[[1,1],[2,2],[3,3],[4,4],[1,3,1,3],[2,4,2,4],[3,4,3,4],[1,2,1,3,2,3],[1,3,4,2,1,2,3,4],[2,1,2,1,2,1,2,1]],nontrivrels=Vector{Int}[[1,3,1,3],[2,4,2,4],[3,4,3,4],[1,2,1,3,2,3],[1,3,4,2,1,2,3,4],[2,1,2,1,2,1,2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,19),(4,12)],ordersubdis=Tuple{Int,Int}[(1,1),(2,19),(4,39),(8,35),(16,15),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"1152",aut_gens=Vector{Vector{Int}}[[[1],[2,1,2,1,2],[3],[4,1,2,1,2]],[[1],[2],[1,2,4],[1,2,3]],[[4],[1],[2],[1,3]]],nchars=17,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C4.C2^3",gens=[perm"(1,17)(2,18)(3,19)(4,20)(5,21)(6,22)(7,23)(8,24)(9,25)(10,26)(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)",perm"(1,10,2,9)(3,12,4,11)(5,14,6,13)(7,16,8,15)(17,25,18,26)(19,27,20,28)(21,29,22,30)(23,31,24,32)",perm"(1,6,2,5)(3,8,4,7)(9,13,10,14)(11,15,12,16)(17,22,18,21)(19,24,20,23)(25,29,26,30)(27,31,28,32)",perm"(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16)(17,20)(18,19)(21,24)(22,23)(25,28)(26,27)(29,32)(30,31)"],rels=Vector{Int}[[1,1],[4,4],[-2,-2,-3,-3],[-2,-3,2,-3],[-2,-2,3,3],[-2,1,-2,1],[1,-3,1,3],[-2,4,2,4],[-3,4,3,4],[3,3,4,1,4,1]],nontrivrels=Vector{Int}[[-2,-2,-3,-3],[-2,-3,2,-3],[-2,-2,3,3],[-2,1,-2,1],[1,-3,1,3],[-2,4,2,4],[-3,4,3,4],[3,3,4,1,4,1]],orderdis=Tuple{Int,Int}[(1,1),(2,11),(4,20)],ordersubdis=Tuple{Int,Int}[(1,1),(2,11),(4,15),(8,35),(16,15),(32,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"1920",aut_gens=Vector{Vector{Int}}[[[1,2],[2],[1,4],[1,3,4]],[[4],[1,3],[2,4],[1,2]]],nchars=17,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2^5",gens=[perm"(1,17)(2,18)(3,19)(4,20)(5,21)(6,22)(7,23)(8,24)(9,25)(10,26)(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)",perm"(1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)(17,25)(18,26)(19,27)(20,28)(21,29)(22,30)(23,31)(24,32)",perm"(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,23)(20,24)(25,29)(26,30)(27,31)(28,32)",perm"(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24)(25,27)(26,28)(29,31)(30,32)",perm"(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)"],rels=Vector{Int}[[1,1],[2,2],[3,3],[4,4],[5,5],[1,2,1,2],[1,3,1,3],[2,3,2,3],[1,4,1,4],[2,4,2,4],[3,4,3,4],[1,5,1,5],[2,5,2,5],[3,5,3,5],[4,5,4,5]],nontrivrels=Vector{Int}[[1,2,1,2],[1,3,1,3],[2,3,2,3],[1,4,1,4],[2,4,2,4],[3,4,3,4],[1,5,1,5],[2,5,2,5],[3,5,3,5],[4,5,4,5]],orderdis=Tuple{Int,Int}[(1,1),(2,31)],ordersubdis=Tuple{Int,Int}[(1,1),(2,31),(4,155),(8,155),(16,31),(32,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"9999360",aut_gens=Vector{Vector{Int}}[[[5],[1],[2],[3],[4]],[[1],[2],[3],[4,5],[5]]],nchars=32,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="C33",gens=[perm"(1,23,12)(2,24,13)(3,25,14)(4,26,15)(5,27,16)(6,28,17)(7,29,18)(8,30,19)(9,31,20)(10,32,21)(11,33,22)",perm"(1,11,10,9,8,7,6,5,4,3,2)(12,22,21,20,19,18,17,16,15,14,13)(23,33,32,31,30,29,28,27,26,25,24)"],rels=Vector{Int}[[1,1,1],[-1,-2,1,2],[2,2,2,2,2,2,2,2,2,2,2]],nontrivrels=Vector{Int}[[-1,-2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(3,2),(11,10),(33,20)],ordersubdis=Tuple{Int,Int}[(1,1),(3,1),(11,1),(33,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"20",aut_gens=Vector{Vector{Int}}[[[1],[-2,-2,-2,-2]],[[-1],[-2]]],nchars=33,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,4,5],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="D17",gens=[perm"(1,18)(2,19)(3,20)(4,21)(5,22)(6,23)(7,24)(8,25)(9,26)(10,27)(11,28)(12,29)(13,30)(14,31)(15,32)(16,33)(17,34)",perm"(1,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2)(18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34)"],rels=Vector{Int}[[1,1],[-2,1,-2,1],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]],nontrivrels=Vector{Int}[[-2,1,-2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,17),(17,16)],ordersubdis=Tuple{Int,Int}[(1,1),(2,17),(17,1),(34,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"272",aut_gens=Vector{Vector{Int}}[[[1,2,2,2,2],[2]],[[1],[-2,-2,-2,-2,-2]]],nchars=10,dims=Int[1,1,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C34",gens=[perm"(1,18)(2,19)(3,20)(4,21)(5,22)(6,23)(7,24)(8,25)(9,26)(10,27)(11,28)(12,29)(13,30)(14,31)(15,32)(16,33)(17,34)",perm"(1,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2)(18,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19)"],rels=Vector{Int}[[1,1],[-2,1,2,1],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]],nontrivrels=Vector{Int}[[-2,1,2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(17,16),(34,16)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(17,1),(34,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"16",aut_gens=Vector{Vector{Int}}[[[1],[2,2,2,2,2,2,2]]],nchars=34,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="C35",gens=[perm"(1,29,22,15,8)(2,30,23,16,9)(3,31,24,17,10)(4,32,25,18,11)(5,33,26,19,12)(6,34,27,20,13)(7,35,28,21,14)",perm"(1,7,6,5,4,3,2)(8,14,13,12,11,10,9)(15,21,20,19,18,17,16)(22,28,27,26,25,24,23)(29,35,34,33,32,31,30)"],rels=Vector{Int}[[-1,-2,1,2],[1,1,1,1,1],[2,2,2,2,2,2,2]],nontrivrels=Vector{Int}[[-1,-2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(5,4),(7,6),(35,24)],ordersubdis=Tuple{Int,Int}[(1,1),(5,1),(7,1),(35,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"24",aut_gens=Vector{Vector{Int}}[[[1],[-2,-2]],[[1,1],[-2]]],nchars=35,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,6,7],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="C9:C4",gens=[perm"(1,28,10,19)(2,29,11,20)(3,30,12,21)(4,31,13,22)(5,32,14,23)(6,33,15,24)(7,34,16,25)(8,35,17,26)(9,36,18,27)",perm"(1,8,5,2,9,6,3,7,4)(10,17,14,11,18,15,12,16,13)(19,22,25,21,24,27,20,23,26)(28,31,34,30,33,36,29,32,35)"],rels=Vector{Int}[[1,1,1,1],[-1,-2,1,-2],[2,2,2,2,2,2,2,2,2]],nontrivrels=Vector{Int}[[-1,-2,1,-2]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(3,2),(4,18),(6,2),(9,6),(18,6)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(3,1),(4,9),(6,1),(9,1),(12,3),(18,1),(36,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"108",aut_gens=Vector{Vector{Int}}[[[1],[-2]],[[1,-2,-2,-2,-2,-2],[2]],[[-1],[2,2]]],nchars=12,dims=Int[1,1,1,1,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,2,1,1,2,2,1,2,1],galrep=Int[1,2,3,5,6,7,8],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C36",gens=[perm"(1,22,4,19)(2,23,5,20)(3,24,6,21)(7,28,10,25)(8,29,11,26)(9,30,12,27)(13,34,16,31)(14,35,17,32)(15,36,18,33)",perm"(1,15,9,3,14,8,2,13,7)(4,18,12,6,17,11,5,16,10)(19,33,27,21,32,26,20,31,25)(22,36,30,24,35,29,23,34,28)"],rels=Vector{Int}[[1,1,1,1],[-1,-2,1,2],[2,2,2,2,2,2,2,2,2]],nontrivrels=Vector{Int}[[-1,-2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(3,2),(4,2),(6,2),(9,6),(12,4),(18,6),(36,12)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(3,1),(4,1),(6,1),(9,1),(12,1),(18,1),(36,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"12",aut_gens=Vector{Vector{Int}}[[[1],[2,2]],[[-1],[2,2]]],nchars=36,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,5,6,7,13,14,15],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2^2:C9",gens=[perm"(1,33,21,9,29,17,5,25,13)(2,34,22,10,30,18,6,26,14)(3,35,23,11,31,19,7,27,15)(4,36,24,12,32,20,8,28,16)",perm"(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)"],rels=Vector{Int}[[2,2],[1,2,-1,2,-1,2,1],[1,1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[[1,2,-1,2,-1,2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(3,2),(6,6),(9,24)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(3,1),(4,1),(6,3),(9,4),(12,1),(36,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"72",aut_gens=Vector{Vector{Int}}[[[1],[-1,2,1]],[[2,1],[2]],[[1,1],[-1,2,1]]],nchars=12,dims=Int[1,1,1,1,1,1,1,1,1,3,3,3],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,4,10,11],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="D18",gens=[perm"(1,19)(2,20)(3,21)(4,22)(5,23)(6,24)(7,25)(8,26)(9,27)(10,28)(11,29)(12,30)(13,31)(14,32)(15,33)(16,34)(17,35)(18,36)",perm"(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17)(9,18)(19,28)(20,29)(21,30)(22,31)(23,32)(24,33)(25,34)(26,35)(27,36)",perm"(1,8,5,2,9,6,3,7,4)(10,17,14,11,18,15,12,16,13)(19,22,25,21,24,27,20,23,26)(28,31,34,30,33,36,29,32,35)"],rels=Vector{Int}[[1,1],[2,2],[1,2,1,2],[1,-3,1,-3],[2,-3,2,3],[3,3,3,3,3,3,3,3,3]],nontrivrels=Vector{Int}[[1,2,1,2],[1,-3,1,-3],[2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,19),(3,2),(6,2),(9,6),(18,6)],ordersubdis=Tuple{Int,Int}[(1,1),(2,19),(3,1),(4,9),(6,7),(9,1),(12,3),(18,3),(36,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"108",aut_gens=Vector{Vector{Int}}[[[1],[2],[-3]],[[1,-3,-3,-3,-3,-3],[2],[3]],[[1,2],[2],[3,3]]],nchars=12,dims=Int[1,1,1,1,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*C18",gens=[perm"(1,19)(2,20)(3,21)(4,22)(5,23)(6,24)(7,25)(8,26)(9,27)(10,28)(11,29)(12,30)(13,31)(14,32)(15,33)(16,34)(17,35)(18,36)",perm"(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17)(9,18)(19,28)(20,29)(21,30)(22,31)(23,32)(24,33)(25,34)(26,35)(27,36)",perm"(1,9,6,3,8,5,2,7,4)(10,18,15,12,17,14,11,16,13)(19,27,24,21,26,23,20,25,22)(28,36,33,30,35,32,29,34,31)"],rels=Vector{Int}[[1,1],[2,2],[1,2,1,2],[1,-3,1,3],[2,-3,2,3],[3,3,3,3,3,3,3,3,3]],nontrivrels=Vector{Int}[[1,2,1,2],[1,-3,1,3],[2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(3,2),(6,6),(9,6),(18,18)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(3,1),(4,1),(6,3),(9,1),(12,1),(18,3),(36,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"36",aut_gens=Vector{Vector{Int}}[[[1],[2],[3,3]],[[1,2],[2],[3,3]],[[2],[1],[3,3]]],nchars=36,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,13,14,15,16],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C3*C3:C4",gens=[perm"(1,22,4,19)(2,23,5,20)(3,24,6,21)(7,28,10,25)(8,29,11,26)(9,30,12,27)(13,34,16,31)(14,35,17,32)(15,36,18,33)",perm"(1,13,7)(2,14,8)(3,15,9)(4,16,10)(5,17,11)(6,18,12)(19,31,25)(20,32,26)(21,33,27)(22,34,28)(23,35,29)(24,36,30)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,20,21)(22,23,24)(25,26,27)(28,29,30)(31,32,33)(34,35,36)"],rels=Vector{Int}[[2,2,2],[3,3,3],[1,1,1,1],[-1,-2,1,2],[-1,-3,1,-3],[-2,-3,2,3]],nontrivrels=Vector{Int}[[-1,-2,1,2],[-1,-3,1,-3],[-2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(3,8),(4,6),(6,8),(12,12)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(3,4),(4,3),(6,4),(9,1),(12,4),(18,1),(36,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"24",aut_gens=Vector{Vector{Int}}[[[1],[2],[-3]],[[1,3],[2],[3]],[[1],[-2],[-3]],[[-1],[-2],[-3]]],nchars=18,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1],galrep=Int[1,2,3,4,7,9,13,14,15,16],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C3^2:C4",gens=[perm"(1,28,10,19)(2,29,11,20)(3,30,12,21)(4,31,13,22)(5,32,14,23)(6,33,15,24)(7,34,16,25)(8,35,17,26)(9,36,18,27)",perm"(1,7,4)(2,8,5)(3,9,6)(10,16,13)(11,17,14)(12,18,15)(19,22,25)(20,23,26)(21,24,27)(28,31,34)(29,32,35)(30,33,36)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,20,21)(22,23,24)(25,26,27)(28,29,30)(31,32,33)(34,35,36)"],rels=Vector{Int}[[2,2,2],[3,3,3],[1,1,1,1],[-1,-2,1,-2],[-1,-3,1,-3],[-2,-3,2,3]],nontrivrels=Vector{Int}[[-1,-2,1,-2],[-1,-3,1,-3],[-2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(3,8),(4,18),(6,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(3,4),(4,9),(6,4),(9,1),(12,12),(18,1),(36,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"864",aut_gens=Vector{Vector{Int}}[[[1,2],[2],[3]],[[1],[-2],[3]],[[1],[-2,-3],[2]],[[-1],[2],[3]]],nchars=12,dims=Int[1,1,1,1,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,2,1,1,2,2,2,1,1],galrep=Int[1,2,3,5,6,7,8,9,10,11,12],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C3*C12",gens=[perm"(1,20,2,19)(3,22,4,21)(5,24,6,23)(7,26,8,25)(9,28,10,27)(11,30,12,29)(13,32,14,31)(15,34,16,33)(17,36,18,35)",perm"(1,13,7)(2,14,8)(3,15,9)(4,16,10)(5,17,11)(6,18,12)(19,31,25)(20,32,26)(21,33,27)(22,34,28)(23,35,29)(24,36,30)",perm"(1,5,3)(2,6,4)(7,11,9)(8,12,10)(13,17,15)(14,18,16)(19,23,21)(20,24,22)(25,29,27)(26,30,28)(31,35,33)(32,36,34)"],rels=Vector{Int}[[2,2,2],[3,3,3],[1,1,1,1],[-1,-2,1,2],[-1,-3,1,3],[-2,-3,2,3]],nontrivrels=Vector{Int}[[-1,-2,1,2],[-1,-3,1,3],[-2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(3,8),(4,2),(6,8),(12,16)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(3,4),(4,1),(6,4),(9,1),(12,4),(18,1),(36,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"96",aut_gens=Vector{Vector{Int}}[[[1],[-2,-3],[2]],[[1],[-2],[3]],[[-1],[2],[3]]],nchars=36,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,5,6,7,13,14,15,17,18,19,21,22,23],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C3:S3.C2",gens=[perm"(1,28,10,19)(2,29,11,20)(3,30,12,21)(4,31,13,22)(5,32,14,23)(6,33,15,24)(7,34,16,25)(8,35,17,26)(9,36,18,27)",perm"(1,7,4)(2,8,5)(3,9,6)(10,13,16)(11,14,17)(12,15,18)(19,26,24)(20,27,22)(21,25,23)(28,33,35)(29,31,36)(30,32,34)"],rels=Vector{Int}[[2,2,2],[1,1,1,1],[1,1,-2,-1,-1,-2],[1,-2,1,-2,1,-2,1,-2],[-2,-1,2,1,2,1,2,-1]],nontrivrels=Vector{Int}[[1,1,-2,-1,-1,-2],[1,-2,1,-2,1,-2,1,-2],[-2,-1,2,1,2,1,2,-1]],orderdis=Tuple{Int,Int}[(1,1),(2,9),(3,8),(4,18)],ordersubdis=Tuple{Int,Int}[(1,1),(2,9),(3,4),(4,9),(6,12),(9,1),(18,1),(36,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"144",aut_gens=Vector{Vector{Int}}[[[2,1],[2]],[[1],[-1,-2,-1,-2,-1,-1]],[[-1],[2,1,1,2,1,2,1]]],nchars=6,dims=Int[1,1,1,1,4,4],schur=Int[1,1,1,1,1,1],galrep=Int[1,2,3,5,6],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="S3^2",gens=[perm"(1,19)(2,20)(3,21)(4,22)(5,23)(6,24)(7,25)(8,26)(9,27)(10,28)(11,29)(12,30)(13,31)(14,32)(15,33)(16,34)(17,35)(18,36)",perm"(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17)(9,18)(19,28)(20,29)(21,30)(22,31)(23,32)(24,33)(25,34)(26,35)(27,36)",perm"(1,7,4)(2,8,5)(3,9,6)(10,13,16)(11,14,17)(12,15,18)(19,25,22)(20,26,23)(21,27,24)(28,31,34)(29,32,35)(30,33,36)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,20,21)(22,23,24)(25,26,27)(28,29,30)(31,32,33)(34,35,36)"],rels=Vector{Int}[[1,1],[2,2],[3,3,3],[4,4,4],[1,2,1,2],[1,-3,1,3],[2,-3,2,-3],[1,-4,1,-4],[2,-4,2,4],[-3,-4,3,4]],nontrivrels=Vector{Int}[[1,2,1,2],[1,-3,1,3],[2,-3,2,-3],[1,-4,1,-4],[2,-4,2,4],[-3,-4,3,4]],orderdis=Tuple{Int,Int}[(1,1),(2,15),(3,8),(6,12)],ordersubdis=Tuple{Int,Int}[(1,1),(2,15),(3,4),(4,9),(6,20),(9,1),(12,6),(18,3),(36,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"72",aut_gens=Vector{Vector{Int}}[[[1],[2],[-3],[4]],[[1,4],[2],[3],[4]],[[2],[1],[-4],[3]]],nchars=9,dims=Int[1,1,1,1,2,2,2,2,4],schur=Int[1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C3*A4",gens=[perm"(1,25,13)(2,26,14)(3,27,15)(4,28,16)(5,29,17)(6,30,18)(7,31,19)(8,32,20)(9,33,21)(10,34,22)(11,35,23)(12,36,24)",perm"(1,9,5)(2,10,6)(3,11,7)(4,12,8)(13,21,17)(14,22,18)(15,23,19)(16,24,20)(25,33,29)(26,34,30)(27,35,31)(28,36,32)",perm"(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)"],rels=Vector{Int}[[3,3],[1,1,1],[2,2,2],[-1,-2,1,2],[-2,3,2,3],[3,-1,3,-1,3,-1]],nontrivrels=Vector{Int}[[-1,-2,1,2],[-2,3,2,3],[3,-1,3,-1,3,-1]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(3,26),(6,6)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(3,13),(4,1),(6,3),(9,4),(12,4),(36,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"144",aut_gens=Vector{Vector{Int}}[[[1],[2],[-1,3,1]],[[3,1],[2],[3]],[[1,2],[2],[3]],[[1],[-2],[3]],[[-1],[-2],[-1,3,1]]],nchars=12,dims=Int[1,1,1,1,1,1,1,1,1,3,3,3],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,4,5,6,10,11],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C6*S3",gens=[perm"(1,19)(2,20)(3,21)(4,22)(5,23)(6,24)(7,25)(8,26)(9,27)(10,28)(11,29)(12,30)(13,31)(14,32)(15,33)(16,34)(17,35)(18,36)",perm"(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17)(9,18)(19,28)(20,29)(21,30)(22,31)(23,32)(24,33)(25,34)(26,35)(27,36)",perm"(1,7,4)(2,8,5)(3,9,6)(10,16,13)(11,17,14)(12,18,15)(19,25,22)(20,26,23)(21,27,24)(28,34,31)(29,35,32)(30,36,33)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,20,21)(22,23,24)(25,26,27)(28,29,30)(31,32,33)(34,35,36)"],rels=Vector{Int}[[1,1],[2,2],[3,3,3],[4,4,4],[1,2,1,2],[1,-3,1,3],[2,-3,2,3],[1,-4,1,-4],[2,-4,2,4],[-3,-4,3,4]],nontrivrels=Vector{Int}[[1,2,1,2],[1,-3,1,3],[2,-3,2,3],[1,-4,1,-4],[2,-4,2,4],[-3,-4,3,4]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(3,8),(6,20)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(3,4),(4,3),(6,12),(9,1),(12,4),(18,3),(36,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"24",aut_gens=Vector{Vector{Int}}[[[1],[2],[3],[-4]],[[1,4],[2],[3],[4]],[[1],[2],[-3],[-4]],[[1,2],[2],[-3],[-4]]],nchars=18,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,8,11,13,14,15,17],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*C3:S3",gens=[perm"(1,19)(2,20)(3,21)(4,22)(5,23)(6,24)(7,25)(8,26)(9,27)(10,28)(11,29)(12,30)(13,31)(14,32)(15,33)(16,34)(17,35)(18,36)",perm"(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17)(9,18)(19,28)(20,29)(21,30)(22,31)(23,32)(24,33)(25,34)(26,35)(27,36)",perm"(1,7,4)(2,8,5)(3,9,6)(10,16,13)(11,17,14)(12,18,15)(19,22,25)(20,23,26)(21,24,27)(28,31,34)(29,32,35)(30,33,36)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,20,21)(22,23,24)(25,26,27)(28,29,30)(31,32,33)(34,35,36)"],rels=Vector{Int}[[1,1],[2,2],[3,3,3],[4,4,4],[1,2,1,2],[1,-3,1,-3],[2,-3,2,3],[1,-4,1,-4],[2,-4,2,4],[-3,-4,3,4]],nontrivrels=Vector{Int}[[1,2,1,2],[1,-3,1,-3],[2,-3,2,3],[1,-4,1,-4],[2,-4,2,4],[-3,-4,3,4]],orderdis=Tuple{Int,Int}[(1,1),(2,19),(3,8),(6,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,19),(3,4),(4,9),(6,28),(9,1),(12,12),(18,3),(36,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"864",aut_gens=Vector{Vector{Int}}[[[1,3],[2],[3],[4]],[[1],[2],[-3],[4]],[[1],[2],[-3,-4],[3]],[[1,2],[2],[3],[4]]],nchars=12,dims=Int[1,1,1,1,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C6^2",gens=[perm"(1,19)(2,20)(3,21)(4,22)(5,23)(6,24)(7,25)(8,26)(9,27)(10,28)(11,29)(12,30)(13,31)(14,32)(15,33)(16,34)(17,35)(18,36)",perm"(1,10)(2,11)(3,12)(4,13)(5,14)(6,15)(7,16)(8,17)(9,18)(19,28)(20,29)(21,30)(22,31)(23,32)(24,33)(25,34)(26,35)(27,36)",perm"(1,7,4)(2,8,5)(3,9,6)(10,16,13)(11,17,14)(12,18,15)(19,25,22)(20,26,23)(21,27,24)(28,34,31)(29,35,32)(30,36,33)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,27,26)(28,30,29)(31,33,32)(34,36,35)"],rels=Vector{Int}[[1,1],[2,2],[3,3,3],[4,4,4],[1,2,1,2],[1,-3,1,3],[2,-3,2,3],[1,-4,1,4],[2,-4,2,4],[-3,-4,3,4]],nontrivrels=Vector{Int}[[1,2,1,2],[1,-3,1,3],[2,-3,2,3],[1,-4,1,4],[2,-4,2,4],[-3,-4,3,4]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(3,8),(6,24)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(3,4),(4,1),(6,12),(9,1),(12,4),(18,3),(36,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"288",aut_gens=Vector{Vector{Int}}[[[1],[2],[-3,-4],[3]],[[1],[2],[-3],[4]],[[1,2],[2],[3],[4]],[[2],[1],[3],[4]]],nchars=36,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,13,14,15,16,17,18,19,20,21,22,23,24],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="C37",gens=[perm"(1,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2)"],rels=Vector{Int}[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[],orderdis=Tuple{Int,Int}[(1,1),(37,36)],ordersubdis=Tuple{Int,Int}[(1,1),(37,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"36",aut_gens=Vector{Vector{Int}}[[[1,1]]],nchars=37,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ 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(name="C38",gens=[perm"(1,20)(2,21)(3,22)(4,23)(5,24)(6,25)(7,26)(8,27)(9,28)(10,29)(11,30)(12,31)(13,32)(14,33)(15,34)(16,35)(17,36)(18,37)(19,38)",perm"(1,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2)(20,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21)"],rels=Vector{Int}[[1,1],[-2,1,2,1],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]],nontrivrels=Vector{Int}[[-2,1,2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(19,18),(38,18)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(19,1),(38,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"18",aut_gens=Vector{Vector{Int}}[[[1],[2,2,2]]],nchars=38,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="C13:C3",gens=[perm"(1,27,14)(2,28,15)(3,29,16)(4,30,17)(5,31,18)(6,32,19)(7,33,20)(8,34,21)(9,35,22)(10,36,23)(11,37,24)(12,38,25)(13,39,26)",perm"(1,13,12,11,10,9,8,7,6,5,4,3,2)(14,24,21,18,15,25,22,19,16,26,23,20,17)(27,31,35,39,30,34,38,29,33,37,28,32,36)"],rels=Vector{Int}[[1,1,1],[-2,-1,-2,-1,-2,-1],[2,-1,-2,1,2,2]],nontrivrels=Vector{Int}[[-2,-1,-2,-1,-2,-1],[2,-1,-2,1,2,2]],orderdis=Tuple{Int,Int}[(1,1),(3,26),(13,12)],ordersubdis=Tuple{Int,Int}[(1,1),(3,13),(13,1),(39,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"156",aut_gens=Vector{Vector{Int}}[[[2,1,2],[2]],[[1],[-1,2,2,1]]],nchars=7,dims=Int[1,1,1,3,3,3,3],schur=Int[1,1,1,1,1,1,1],galrep=Int[1,2,4],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C39",gens=[perm"(1,27,14)(2,28,15)(3,29,16)(4,30,17)(5,31,18)(6,32,19)(7,33,20)(8,34,21)(9,35,22)(10,36,23)(11,37,24)(12,38,25)(13,39,26)",perm"(1,13,12,11,10,9,8,7,6,5,4,3,2)(14,26,25,24,23,22,21,20,19,18,17,16,15)(27,39,38,37,36,35,34,33,32,31,30,29,28)"],rels=Vector{Int}[[1,1,1],[-1,-2,1,2],[2,2,2,2,2,2,2,2,2,2,2,2,2]],nontrivrels=Vector{Int}[[-1,-2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(3,2),(13,12),(39,24)],ordersubdis=Tuple{Int,Int}[(1,1),(3,1),(13,1),(39,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"24",aut_gens=Vector{Vector{Int}}[[[1],[-2,-2]],[[-1],[-2]]],nchars=39,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,4,5],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="C5:C8",gens=[perm"(1,36,16,26,6,31,11,21)(2,37,17,27,7,32,12,22)(3,38,18,28,8,33,13,23)(4,39,19,29,9,34,14,24)(5,40,20,30,10,35,15,25)",perm"(1,5,4,3,2)(6,10,9,8,7)(11,15,14,13,12)(16,20,19,18,17)(21,22,23,24,25)(26,27,28,29,30)(31,32,33,34,35)(36,37,38,39,40)"],rels=Vector{Int}[[-1,-2,1,-2],[2,2,2,2,2],[1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[[-1,-2,1,-2]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(4,2),(5,4),(8,20),(10,4),(20,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(4,1),(5,1),(8,5),(10,1),(20,1),(40,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"80",aut_gens=Vector{Vector{Int}}[[[1,-2],[2]],[[1],[-2,-2]],[[1,1,1,1,1],[-2]],[[1,1,1],[-2]]],nchars=16,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2],galrep=Int[1,2,3,5,9,11,13],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C40",gens=[perm"(1,24,4,22,2,23,3,21)(5,28,8,26,6,27,7,25)(9,32,12,30,10,31,11,29)(13,36,16,34,14,35,15,33)(17,40,20,38,18,39,19,37)",perm"(1,17,13,9,5)(2,18,14,10,6)(3,19,15,11,7)(4,20,16,12,8)(21,37,33,29,25)(22,38,34,30,26)(23,39,35,31,27)(24,40,36,32,28)"],rels=Vector{Int}[[-1,-2,1,2],[2,2,2,2,2],[1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[[-1,-2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(4,2),(5,4),(8,4),(10,4),(20,8),(40,16)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(4,1),(5,1),(8,1),(10,1),(20,1),(40,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"16",aut_gens=Vector{Vector{Int}}[[[1],[2,2]],[[1,1,1,1,1],[-2]],[[1,1,1],[-2]]],nchars=40,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,5,9,10,11,13],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C10.C4",gens=[perm"(1,36,16,26,6,31,11,21)(2,37,17,27,7,32,12,22)(3,38,18,28,8,33,13,23)(4,39,19,29,9,34,14,24)(5,40,20,30,10,35,15,25)",perm"(1,5,4,3,2)(6,10,9,8,7)(11,12,13,14,15)(16,17,18,19,20)(21,24,22,25,23)(26,29,27,30,28)(31,33,35,32,34)(36,38,40,37,39)"],rels=Vector{Int}[[-1,-2,1,2,2],[2,2,2,2,2],[1,-2,-1,-2,-2],[1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[[-1,-2,1,2,2],[1,-2,-1,-2,-2]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(4,10),(5,4),(8,20),(10,4)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(4,5),(5,1),(8,5),(10,1),(20,1),(40,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"40",aut_gens=Vector{Vector{Int}}[[[1],[2,2]],[[1,2],[2]],[[1,1,1,1,1],[-2]]],nchars=10,dims=Int[1,1,1,1,1,1,1,1,4,4],schur=Int[1,1,1,1,1,1,1,1,1,2],galrep=Int[1,2,3,5,9,10],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C5:Q8",gens=[perm"(1,26,6,21)(2,27,7,22)(3,28,8,23)(4,29,9,24)(5,30,10,25)(11,36,16,31)(12,37,17,32)(13,38,18,33)(14,39,19,34)(15,40,20,35)",perm"(1,16,6,11)(2,17,7,12)(3,18,8,13)(4,19,9,14)(5,20,10,15)(21,31,26,36)(22,32,27,37)(23,33,28,38)(24,34,29,39)(25,35,30,40)",perm"(1,5,4,3,2)(6,10,9,8,7)(11,15,14,13,12)(16,20,19,18,17)(21,22,23,24,25)(26,27,28,29,30)(31,32,33,34,35)(36,37,38,39,40)"],rels=Vector{Int}[[-1,-1,-2,-2],[-1,-2,1,-2],[-1,-1,2,2],[-1,-3,1,-3],[-2,-3,2,3],[3,3,3,3,3]],nontrivrels=Vector{Int}[[-1,-1,-2,-2],[-1,-2,1,-2],[-1,-1,2,2],[-1,-3,1,-3],[-2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(4,22),(5,4),(10,4),(20,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(4,11),(5,1),(8,5),(10,1),(20,3),(40,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"160",aut_gens=Vector{Vector{Int}}[[[1],[-2],[-3]],[[1,-3,-3],[2],[3]],[[1],[2],[3,3]],[[1,2],[2],[-3]]],nchars=13,dims=Int[1,1,1,1,2,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,2,1,1,1,1,2,2,2,2],galrep=Int[1,2,3,4,5,6,7,10],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C4*D5",gens=[perm"(1,21)(2,22)(3,23)(4,24)(5,25)(6,26)(7,27)(8,28)(9,29)(10,30)(11,31)(12,32)(13,33)(14,34)(15,35)(16,36)(17,37)(18,38)(19,39)(20,40)",perm"(1,16,6,11)(2,17,7,12)(3,18,8,13)(4,19,9,14)(5,20,10,15)(21,36,26,31)(22,37,27,32)(23,38,28,33)(24,39,29,34)(25,40,30,35)",perm"(1,5,4,3,2)(6,10,9,8,7)(11,15,14,13,12)(16,20,19,18,17)(21,22,23,24,25)(26,27,28,29,30)(31,32,33,34,35)(36,37,38,39,40)"],rels=Vector{Int}[[1,1],[2,2,2,2],[-2,1,2,1],[-2,-3,2,3],[1,-3,1,-3],[3,3,3,3,3]],nontrivrels=Vector{Int}[[-2,1,2,1],[-2,-3,2,3],[1,-3,1,-3]],orderdis=Tuple{Int,Int}[(1,1),(2,11),(4,12),(5,4),(10,4),(20,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,11),(4,11),(5,1),(8,5),(10,3),(20,3),(40,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"80",aut_gens=Vector{Vector{Int}}[[[1,-3],[2],[3]],[[1],[2],[3,3]],[[1,-2,-2],[2],[-3]],[[1],[-2],[-3]]],nchars=16,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,9,10,13],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="D20",gens=[perm"(1,21)(2,22)(3,23)(4,24)(5,25)(6,26)(7,27)(8,28)(9,29)(10,30)(11,31)(12,32)(13,33)(14,34)(15,35)(16,36)(17,37)(18,38)(19,39)(20,40)",perm"(1,16,6,11)(2,17,7,12)(3,18,8,13)(4,19,9,14)(5,20,10,15)(21,31,26,36)(22,32,27,37)(23,33,28,38)(24,34,29,39)(25,35,30,40)",perm"(1,5,4,3,2)(6,10,9,8,7)(11,15,14,13,12)(16,20,19,18,17)(21,22,23,24,25)(26,27,28,29,30)(31,32,33,34,35)(36,37,38,39,40)"],rels=Vector{Int}[[1,1],[2,2,2,2],[-2,1,-2,1],[-2,-3,2,3],[1,-3,1,-3],[3,3,3,3,3]],nontrivrels=Vector{Int}[[-2,1,-2,1],[-2,-3,2,3],[1,-3,1,-3]],orderdis=Tuple{Int,Int}[(1,1),(2,21),(4,2),(5,4),(10,4),(20,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,21),(4,11),(5,1),(8,5),(10,5),(20,3),(40,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"160",aut_gens=Vector{Vector{Int}}[[[1],[-2],[-3]],[[1,-3,-3],[2],[3]],[[1],[2],[-3,-3]],[[1,2],[2],[-3]]],nchars=13,dims=Int[1,1,1,1,2,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,10],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*C5:C4",gens=[perm"(1,26,6,21)(2,27,7,22)(3,28,8,23)(4,29,9,24)(5,30,10,25)(11,36,16,31)(12,37,17,32)(13,38,18,33)(14,39,19,34)(15,40,20,35)",perm"(1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20)(21,31)(22,32)(23,33)(24,34)(25,35)(26,36)(27,37)(28,38)(29,39)(30,40)",perm"(1,5,4,3,2)(6,10,9,8,7)(11,15,14,13,12)(16,20,19,18,17)(21,22,23,24,25)(26,27,28,29,30)(31,32,33,34,35)(36,37,38,39,40)"],rels=Vector{Int}[[2,2],[1,1,1,1],[-1,2,1,2],[-1,-3,1,-3],[2,-3,2,3],[3,3,3,3,3]],nontrivrels=Vector{Int}[[-1,2,1,2],[-1,-3,1,-3],[2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(4,20),(5,4),(10,12)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(4,11),(5,1),(8,5),(10,3),(20,3),(40,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"160",aut_gens=Vector{Vector{Int}}[[[1,-3],[2],[3]],[[1],[2],[-3,-3]],[[1],[2,-1,-1],[-3]],[[1,2],[2],[-3]]],nchars=16,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,2,2,1,1,1,1,2,2],galrep=Int[1,2,3,4,5,7,9,10,11,12],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C5:D4",gens=[perm"(1,21)(2,22)(3,23)(4,24)(5,25)(6,26)(7,27)(8,28)(9,29)(10,30)(11,31)(12,32)(13,33)(14,34)(15,35)(16,36)(17,37)(18,38)(19,39)(20,40)",perm"(1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20)(21,36)(22,37)(23,38)(24,39)(25,40)(26,31)(27,32)(28,33)(29,34)(30,35)",perm"(1,5,4,3,2)(6,10,9,8,7)(11,15,14,13,12)(16,20,19,18,17)(21,22,23,24,25)(26,27,28,29,30)(31,32,33,34,35)(36,37,38,39,40)"],rels=Vector{Int}[[1,1],[2,2],[1,-3,1,-3],[2,-3,2,3],[3,3,3,3,3],[1,2,1,2,1,2,1,2]],nontrivrels=Vector{Int}[[1,-3,1,-3],[2,-3,2,3],[1,2,1,2,1,2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,13),(4,10),(5,4),(10,12)],ordersubdis=Tuple{Int,Int}[(1,1),(2,13),(4,11),(5,1),(8,5),(10,5),(20,3),(40,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"80",aut_gens=Vector{Vector{Int}}[[[1],[2,1,2,1,2],[-3]],[[1,1,2,1,2],[2],[3]],[[1,-3,-3],[2],[3]],[[1],[2],[3,3]]],nchars=13,dims=Int[1,1,1,1,2,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,11],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*C20",gens=[perm"(1,22,2,21)(3,24,4,23)(5,26,6,25)(7,28,8,27)(9,30,10,29)(11,32,12,31)(13,34,14,33)(15,36,16,35)(17,38,18,37)(19,40,20,39)",perm"(1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20)(21,31)(22,32)(23,33)(24,34)(25,35)(26,36)(27,37)(28,38)(29,39)(30,40)",perm"(1,9,7,5,3)(2,10,8,6,4)(11,19,17,15,13)(12,20,18,16,14)(21,29,27,25,23)(22,30,28,26,24)(31,39,37,35,33)(32,40,38,36,34)"],rels=Vector{Int}[[2,2],[1,1,1,1],[-1,2,1,2],[-1,-3,1,3],[2,-3,2,3],[3,3,3,3,3]],nontrivrels=Vector{Int}[[-1,2,1,2],[-1,-3,1,3],[2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(4,4),(5,4),(10,12),(20,16)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(4,3),(5,1),(8,1),(10,3),(20,3),(40,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"32",aut_gens=Vector{Vector{Int}}[[[1],[2],[-3,-3]],[[1],[2,-1,-1],[-3]],[[1,2],[2],[-3]]],nchars=40,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,9,10,11,12,13,14],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C5*D4",gens=[perm"(1,21)(2,22)(3,23)(4,24)(5,25)(6,26)(7,27)(8,28)(9,29)(10,30)(11,31)(12,32)(13,33)(14,34)(15,35)(16,36)(17,37)(18,38)(19,39)(20,40)",perm"(1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20)(21,32)(22,31)(23,34)(24,33)(25,36)(26,35)(27,38)(28,37)(29,40)(30,39)",perm"(1,9,7,5,3)(2,10,8,6,4)(11,19,17,15,13)(12,20,18,16,14)(21,29,27,25,23)(22,30,28,26,24)(31,39,37,35,33)(32,40,38,36,34)"],rels=Vector{Int}[[1,1],[2,2],[1,-3,1,3],[2,-3,2,3],[3,3,3,3,3],[1,2,1,2,1,2,1,2]],nontrivrels=Vector{Int}[[1,-3,1,3],[2,-3,2,3],[1,2,1,2,1,2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,5),(4,2),(5,4),(10,20),(20,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,5),(4,3),(5,1),(8,1),(10,5),(20,3),(40,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"32",aut_gens=Vector{Vector{Int}}[[[1],[2,1,2,1,2],[3]],[[1],[2],[-3,-3]],[[2],[1],[-3]]],nchars=25,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,21,22],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C5*Q8",gens=[perm"(1,22,2,21)(3,24,4,23)(5,26,6,25)(7,28,8,27)(9,30,10,29)(11,32,12,31)(13,34,14,33)(15,36,16,35)(17,38,18,37)(19,40,20,39)",perm"(1,12,2,11)(3,14,4,13)(5,16,6,15)(7,18,8,17)(9,20,10,19)(21,31,22,32)(23,33,24,34)(25,35,26,36)(27,37,28,38)(29,39,30,40)",perm"(1,9,7,5,3)(2,10,8,6,4)(11,19,17,15,13)(12,20,18,16,14)(21,29,27,25,23)(22,30,28,26,24)(31,39,37,35,33)(32,40,38,36,34)"],rels=Vector{Int}[[-1,-1,-2,-2],[-1,-2,1,-2],[-1,-1,2,2],[-1,-3,1,3],[-2,-3,2,3],[3,3,3,3,3]],nontrivrels=Vector{Int}[[-1,-1,-2,-2],[-1,-2,1,-2],[-1,-1,2,2],[-1,-3,1,3],[-2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(4,6),(5,4),(10,4),(20,24)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(4,3),(5,1),(8,1),(10,1),(20,3),(40,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"96",aut_gens=Vector{Vector{Int}}[[[1],[2],[3,3]],[[1,2],[2],[-3]],[[2],[1],[-3]]],nchars=25,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1],galrep=Int[1,2,3,4,5,6,8,15,21,22],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*F5",gens=[perm"(1,26,6,21)(2,27,7,22)(3,28,8,23)(4,29,9,24)(5,30,10,25)(11,36,16,31)(12,37,17,32)(13,38,18,33)(14,39,19,34)(15,40,20,35)",perm"(1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20)(21,31)(22,32)(23,33)(24,34)(25,35)(26,36)(27,37)(28,38)(29,39)(30,40)",perm"(1,5,4,3,2)(6,7,8,9,10)(11,15,14,13,12)(16,17,18,19,20)(21,24,22,25,23)(26,28,30,27,29)(31,34,32,35,33)(36,38,40,37,39)"],rels=Vector{Int}[[2,2],[1,1,1,1],[-1,2,1,2],[2,-3,2,3],[3,3,3,3,3],[1,-3,-1,-3,-3],[1,1,-3,-1,-1,-3]],nontrivrels=Vector{Int}[[-1,2,1,2],[2,-3,2,3],[1,-3,-1,-3,-3],[1,1,-3,-1,-1,-3]],orderdis=Tuple{Int,Int}[(1,1),(2,11),(4,20),(5,4),(10,4)],ordersubdis=Tuple{Int,Int}[(1,1),(2,11),(4,15),(5,1),(8,5),(10,3),(20,3),(40,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"40",aut_gens=Vector{Vector{Int}}[[[1],[2],[3,3]],[[1,3],[2],[3]],[[1,2],[2],[-3]]],nchars=10,dims=Int[1,1,1,1,1,1,1,1,4,4],schur=Int[1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,7,9,10],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2^2*D5",gens=[perm"(1,21)(2,22)(3,23)(4,24)(5,25)(6,26)(7,27)(8,28)(9,29)(10,30)(11,31)(12,32)(13,33)(14,34)(15,35)(16,36)(17,37)(18,38)(19,39)(20,40)",perm"(1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20)(21,31)(22,32)(23,33)(24,34)(25,35)(26,36)(27,37)(28,38)(29,39)(30,40)",perm"(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20)(21,26)(22,27)(23,28)(24,29)(25,30)(31,36)(32,37)(33,38)(34,39)(35,40)",perm"(1,5,4,3,2)(6,10,9,8,7)(11,15,14,13,12)(16,20,19,18,17)(21,22,23,24,25)(26,27,28,29,30)(31,32,33,34,35)(36,37,38,39,40)"],rels=Vector{Int}[[1,1],[2,2],[3,3],[1,2,1,2],[1,3,1,3],[2,3,2,3],[1,-4,1,-4],[2,-4,2,4],[3,-4,3,4],[4,4,4,4,4]],nontrivrels=Vector{Int}[[1,2,1,2],[1,3,1,3],[2,3,2,3],[1,-4,1,-4],[2,-4,2,4],[3,-4,3,4]],orderdis=Tuple{Int,Int}[(1,1),(2,23),(5,4),(10,12)],ordersubdis=Tuple{Int,Int}[(1,1),(2,23),(4,31),(5,1),(8,5),(10,7),(20,7),(40,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"480",aut_gens=Vector{Vector{Int}}[[[1,-4],[2],[3],[4]],[[1],[2],[3],[4,4]],[[1,3],[2],[3],[-4]],[[1],[3],[2],[-4]],[[1],[2,3],[3],[-4]]],nchars=16,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2^2*C10",gens=[perm"(1,21)(2,22)(3,23)(4,24)(5,25)(6,26)(7,27)(8,28)(9,29)(10,30)(11,31)(12,32)(13,33)(14,34)(15,35)(16,36)(17,37)(18,38)(19,39)(20,40)",perm"(1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20)(21,31)(22,32)(23,33)(24,34)(25,35)(26,36)(27,37)(28,38)(29,39)(30,40)",perm"(1,6)(2,7)(3,8)(4,9)(5,10)(11,16)(12,17)(13,18)(14,19)(15,20)(21,26)(22,27)(23,28)(24,29)(25,30)(31,36)(32,37)(33,38)(34,39)(35,40)",perm"(1,5,4,3,2)(6,10,9,8,7)(11,15,14,13,12)(16,20,19,18,17)(21,25,24,23,22)(26,30,29,28,27)(31,35,34,33,32)(36,40,39,38,37)"],rels=Vector{Int}[[1,1],[2,2],[3,3],[1,2,1,2],[1,3,1,3],[2,3,2,3],[1,-4,1,4],[2,-4,2,4],[3,-4,3,4],[4,4,4,4,4]],nontrivrels=Vector{Int}[[1,2,1,2],[1,3,1,3],[2,3,2,3],[1,-4,1,4],[2,-4,2,4],[3,-4,3,4]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(5,4),(10,28)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(4,7),(5,1),(8,1),(10,7),(20,7),(40,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"672",aut_gens=Vector{Vector{Int}}[[[1],[2],[3],[-4,-4]],[[1,2],[2],[3],[-4]],[[3],[1],[2],[-4]]],nchars=40,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="C41",gens=[perm"(1,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2)"],rels=Vector{Int}[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[],orderdis=Tuple{Int,Int}[(1,1),(41,40)],ordersubdis=Tuple{Int,Int}[(1,1),(41,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"40",aut_gens=Vector{Vector{Int}}[[[1,1,1,1,1,1]]],nchars=41,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) ], [ (name="F7",gens=[perm"(1,22)(2,23)(3,24)(4,25)(5,26)(6,27)(7,28)(8,29)(9,30)(10,31)(11,32)(12,33)(13,34)(14,35)(15,36)(16,37)(17,38)(18,39)(19,40)(20,41)(21,42)",perm"(1,15,8)(2,16,9)(3,17,10)(4,18,11)(5,19,12)(6,20,13)(7,21,14)(22,36,29)(23,37,30)(24,38,31)(25,39,32)(26,40,33)(27,41,34)(28,42,35)",perm"(1,7,6,5,4,3,2)(8,13,11,9,14,12,10)(15,18,21,17,20,16,19)(22,23,24,25,26,27,28)(29,31,33,35,30,32,34)(36,40,37,41,38,42,39)"],rels=Vector{Int}[[1,1],[2,2,2],[-2,1,2,1],[1,-3,1,-3],[-3,-3,-2,3,2]],nontrivrels=Vector{Int}[[-2,1,2,1],[1,-3,1,-3],[-3,-3,-2,3,2]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(3,14),(6,14),(7,6)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(3,7),(6,7),(7,1),(14,1),(21,1),(42,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"42",aut_gens=Vector{Vector{Int}}[[[1],[2],[-3]],[[1],[2],[2,3,-2]],[[1,2,3,-2],[-3,2],[3]]],nchars=7,dims=Int[1,1,1,1,1,1,6],schur=Int[1,1,1,1,1,1,1],galrep=Int[1,2,3,4,7],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*C7:C3",gens=[perm"(1,22)(2,23)(3,24)(4,25)(5,26)(6,27)(7,28)(8,29)(9,30)(10,31)(11,32)(12,33)(13,34)(14,35)(15,36)(16,37)(17,38)(18,39)(19,40)(20,41)(21,42)",perm"(1,15,8)(2,16,9)(3,17,10)(4,18,11)(5,19,12)(6,20,13)(7,21,14)(22,36,29)(23,37,30)(24,38,31)(25,39,32)(26,40,33)(27,41,34)(28,42,35)",perm"(1,7,6,5,4,3,2)(8,13,11,9,14,12,10)(15,18,21,17,20,16,19)(22,28,27,26,25,24,23)(29,34,32,30,35,33,31)(36,39,42,38,41,37,40)"],rels=Vector{Int}[[1,1],[2,2,2],[-2,1,2,1],[1,-3,1,3],[-3,-3,-2,3,2]],nontrivrels=Vector{Int}[[-2,1,2,1],[1,-3,1,3],[-3,-3,-2,3,2]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(3,14),(6,14),(7,6),(14,6)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(3,7),(6,7),(7,1),(14,1),(21,1),(42,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"42",aut_gens=Vector{Vector{Int}}[[[1],[2,3],[3]],[[1],[2],[2,-3,-2]]],nchars=10,dims=Int[1,1,1,1,1,1,3,3,3,3],schur=Int[1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,7,8],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C7*S3",gens=[perm"(1,22)(2,23)(3,24)(4,25)(5,26)(6,27)(7,28)(8,29)(9,30)(10,31)(11,32)(12,33)(13,34)(14,35)(15,36)(16,37)(17,38)(18,39)(19,40)(20,41)(21,42)",perm"(1,19,16,13,10,7,4)(2,20,17,14,11,8,5)(3,21,18,15,12,9,6)(22,40,37,34,31,28,25)(23,41,38,35,32,29,26)(24,42,39,36,33,30,27)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,23,24)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)(40,41,42)"],rels=Vector{Int}[[1,1],[3,3,3],[-2,1,2,1],[-2,-3,2,3],[1,-3,1,-3],[2,2,2,2,2,2,2]],nontrivrels=Vector{Int}[[-2,1,2,1],[-2,-3,2,3],[1,-3,1,-3]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(3,2),(7,6),(14,18),(21,12)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(3,1),(6,1),(7,1),(14,3),(21,1),(42,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"36",aut_gens=Vector{Vector{Int}}[[[1],[2],[-3]],[[1,3],[2],[3]],[[1],[2,2,2],[-3]]],nchars=21,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,15,16],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C3*D7",gens=[perm"(1,22)(2,23)(3,24)(4,25)(5,26)(6,27)(7,28)(8,29)(9,30)(10,31)(11,32)(12,33)(13,34)(14,35)(15,36)(16,37)(17,38)(18,39)(19,40)(20,41)(21,42)",perm"(1,15,8)(2,16,9)(3,17,10)(4,18,11)(5,19,12)(6,20,13)(7,21,14)(22,36,29)(23,37,30)(24,38,31)(25,39,32)(26,40,33)(27,41,34)(28,42,35)",perm"(1,7,6,5,4,3,2)(8,14,13,12,11,10,9)(15,21,20,19,18,17,16)(22,23,24,25,26,27,28)(29,30,31,32,33,34,35)(36,37,38,39,40,41,42)"],rels=Vector{Int}[[1,1],[2,2,2],[-2,1,2,1],[-2,-3,2,3],[1,-3,1,-3],[3,3,3,3,3,3,3]],nontrivrels=Vector{Int}[[-2,1,2,1],[-2,-3,2,3],[1,-3,1,-3]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(3,2),(6,14),(7,6),(21,12)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(3,1),(6,7),(7,1),(14,1),(21,1),(42,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"84",aut_gens=Vector{Vector{Int}}[[[1,-3,-3,-3],[2],[3]],[[1],[2],[-3,-3]],[[1],[-2],[-3]]],nchars=15,dims=Int[1,1,1,1,1,1,2,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,7,10],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="D21",gens=[perm"(1,22)(2,23)(3,24)(4,25)(5,26)(6,27)(7,28)(8,29)(9,30)(10,31)(11,32)(12,33)(13,34)(14,35)(15,36)(16,37)(17,38)(18,39)(19,40)(20,41)(21,42)",perm"(1,15,8)(2,16,9)(3,17,10)(4,18,11)(5,19,12)(6,20,13)(7,21,14)(22,29,36)(23,30,37)(24,31,38)(25,32,39)(26,33,40)(27,34,41)(28,35,42)",perm"(1,7,6,5,4,3,2)(8,14,13,12,11,10,9)(15,21,20,19,18,17,16)(22,23,24,25,26,27,28)(29,30,31,32,33,34,35)(36,37,38,39,40,41,42)"],rels=Vector{Int}[[1,1],[2,2,2],[-2,1,-2,1],[-2,-3,2,3],[1,-3,1,-3],[3,3,3,3,3,3,3]],nontrivrels=Vector{Int}[[-2,1,-2,1],[-2,-3,2,3],[1,-3,1,-3]],orderdis=Tuple{Int,Int}[(1,1),(2,21),(3,2),(7,6),(21,12)],ordersubdis=Tuple{Int,Int}[(1,1),(2,21),(3,1),(6,7),(7,1),(14,3),(21,1),(42,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"252",aut_gens=Vector{Vector{Int}}[[[1],[-2],[-3]],[[1,2],[2],[3]],[[1,-3,-3],[2],[3]],[[1],[2],[3,3,3]]],nchars=12,dims=Int[1,1,2,2,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,7],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C42",gens=[perm"(1,22)(2,23)(3,24)(4,25)(5,26)(6,27)(7,28)(8,29)(9,30)(10,31)(11,32)(12,33)(13,34)(14,35)(15,36)(16,37)(17,38)(18,39)(19,40)(20,41)(21,42)",perm"(1,15,8)(2,16,9)(3,17,10)(4,18,11)(5,19,12)(6,20,13)(7,21,14)(22,36,29)(23,37,30)(24,38,31)(25,39,32)(26,40,33)(27,41,34)(28,42,35)",perm"(1,7,6,5,4,3,2)(8,14,13,12,11,10,9)(15,21,20,19,18,17,16)(22,28,27,26,25,24,23)(29,35,34,33,32,31,30)(36,42,41,40,39,38,37)"],rels=Vector{Int}[[1,1],[2,2,2],[-2,1,2,1],[-2,-3,2,3],[1,-3,1,3],[3,3,3,3,3,3,3]],nontrivrels=Vector{Int}[[-2,1,2,1],[-2,-3,2,3],[1,-3,1,3]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(3,2),(6,2),(7,6),(14,6),(21,12),(42,12)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(3,1),(6,1),(7,1),(14,1),(21,1),(42,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"12",aut_gens=Vector{Vector{Int}}[[[1],[2],[-3,-3]],[[1],[-2],[-3]]],nchars=42,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,7,8,9,10],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) 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(name="C44",gens=[perm"(1,24,2,23)(3,26,4,25)(5,28,6,27)(7,30,8,29)(9,32,10,31)(11,34,12,33)(13,36,14,35)(15,38,16,37)(17,40,18,39)(19,42,20,41)(21,44,22,43)",perm"(1,21,19,17,15,13,11,9,7,5,3)(2,22,20,18,16,14,12,10,8,6,4)(23,43,41,39,37,35,33,31,29,27,25)(24,44,42,40,38,36,34,32,30,28,26)"],rels=Vector{Int}[[1,1,1,1],[-1,-2,1,2],[2,2,2,2,2,2,2,2,2,2,2]],nontrivrels=Vector{Int}[[-1,-2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(4,2),(11,10),(22,10),(44,20)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(4,1),(11,1),(22,1),(44,1)],isabelian=true,iscyclic=true,issolvable=true,isnilpotent=true,autorder=big"20",aut_gens=Vector{Vector{Int}}[[[1],[-2,-2,-2,-2]],[[-1],[-2]]],nchars=44,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,5,6,7],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="D22",gens=[perm"(1,23)(2,24)(3,25)(4,26)(5,27)(6,28)(7,29)(8,30)(9,31)(10,32)(11,33)(12,34)(13,35)(14,36)(15,37)(16,38)(17,39)(18,40)(19,41)(20,42)(21,43)(22,44)",perm"(1,12)(2,13)(3,14)(4,15)(5,16)(6,17)(7,18)(8,19)(9,20)(10,21)(11,22)(23,34)(24,35)(25,36)(26,37)(27,38)(28,39)(29,40)(30,41)(31,42)(32,43)(33,44)",perm"(1,11,10,9,8,7,6,5,4,3,2)(12,22,21,20,19,18,17,16,15,14,13)(23,24,25,26,27,28,29,30,31,32,33)(34,35,36,37,38,39,40,41,42,43,44)"],rels=Vector{Int}[[1,1],[2,2],[1,2,1,2],[1,-3,1,-3],[2,-3,2,3],[3,3,3,3,3,3,3,3,3,3,3]],nontrivrels=Vector{Int}[[1,2,1,2],[1,-3,1,-3],[2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,23),(11,10),(22,10)],ordersubdis=Tuple{Int,Int}[(1,1),(2,23),(4,11),(11,1),(22,3),(44,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"220",aut_gens=Vector{Vector{Int}}[[[1,3,3,3,3],[2],[3]],[[1],[2],[3,3]],[[1,2],[2],[-3]]],nchars=14,dims=Int[1,1,1,1,2,2,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*C22",gens=[perm"(1,23)(2,24)(3,25)(4,26)(5,27)(6,28)(7,29)(8,30)(9,31)(10,32)(11,33)(12,34)(13,35)(14,36)(15,37)(16,38)(17,39)(18,40)(19,41)(20,42)(21,43)(22,44)",perm"(1,12)(2,13)(3,14)(4,15)(5,16)(6,17)(7,18)(8,19)(9,20)(10,21)(11,22)(23,34)(24,35)(25,36)(26,37)(27,38)(28,39)(29,40)(30,41)(31,42)(32,43)(33,44)",perm"(1,11,10,9,8,7,6,5,4,3,2)(12,22,21,20,19,18,17,16,15,14,13)(23,33,32,31,30,29,28,27,26,25,24)(34,44,43,42,41,40,39,38,37,36,35)"],rels=Vector{Int}[[1,1],[2,2],[1,2,1,2],[1,-3,1,3],[2,-3,2,3],[3,3,3,3,3,3,3,3,3,3,3]],nontrivrels=Vector{Int}[[1,2,1,2],[1,-3,1,3],[2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(11,10),(22,30)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(4,1),(11,1),(22,3),(44,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"60",aut_gens=Vector{Vector{Int}}[[[1],[2],[-3,-3,-3,-3,-3]],[[1,2],[2],[-3]],[[2],[1],[-3]]],nchars=44,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]) 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(name="C8*S3",gens=[perm"(1,25)(2,26)(3,27)(4,28)(5,29)(6,30)(7,31)(8,32)(9,33)(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)",perm"(1,22,10,16,4,19,7,13)(2,23,11,17,5,20,8,14)(3,24,12,18,6,21,9,15)(25,46,34,40,28,43,31,37)(26,47,35,41,29,44,32,38)(27,48,36,42,30,45,33,39)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)(40,41,42)(43,44,45)(46,47,48)"],rels=Vector{Int}[[1,1],[3,3,3],[-2,1,2,1],[-2,-3,2,3],[1,-3,1,-3],[2,2,2,2,2,2,2,2]],nontrivrels=Vector{Int}[[-2,1,2,1],[-2,-3,2,3],[1,-3,1,-3]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(3,2),(4,8),(6,2),(8,16),(12,4),(24,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(3,1),(4,7),(6,3),(8,7),(12,3),(16,3),(24,3),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"48",aut_gens=Vector{Vector{Int}}[[[1],[2],[-3]],[[1,3],[2],[3]],[[1,2,2,2,2],[2],[-3]],[[1],[2,2,2,2,2],[-3]],[[1],[2,2,2],[-3]]],nchars=24,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,9,10,17,18,19,21],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C24:C2",gens=[perm"(1,25)(2,26)(3,27)(4,28)(5,29)(6,30)(7,31)(8,32)(9,33)(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)",perm"(1,22,10,16,4,19,7,13)(2,23,11,17,5,20,8,14)(3,24,12,18,6,21,9,15)(25,43,34,37,28,46,31,40)(26,44,35,38,29,47,32,41)(27,45,36,39,30,48,33,42)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)(40,41,42)(43,44,45)(46,47,48)"],rels=Vector{Int}[[1,1],[3,3,3],[-2,-3,2,3],[1,-3,1,-3],[-2,-2,-2,1,-2,1],[2,1,2,1,2,2],[-2,-2,-2,-2,1,2,1,-2]],nontrivrels=Vector{Int}[[-2,-3,2,3],[1,-3,1,-3],[-2,-2,-2,1,-2,1],[2,1,2,1,2,2],[-2,-2,-2,-2,1,2,1,-2]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(3,2),(4,8),(6,2),(8,16),(12,4),(24,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(3,1),(4,7),(6,3),(8,7),(12,3),(16,3),(24,3),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"48",aut_gens=Vector{Vector{Int}}[[[1],[2,2,2,2,2],[-3]],[[1,2,2,2,2],[2],[3]],[[1,-3],[2],[3]],[[1],[2],[-3]],[[1],[2,2,2],[-3]]],nchars=18,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,9,10,11,12,15],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C8:S3",gens=[perm"(1,25)(2,26)(3,27)(4,28)(5,29)(6,30)(7,31)(8,32)(9,33)(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)",perm"(1,22,10,16,4,19,7,13)(2,23,11,17,5,20,8,14)(3,24,12,18,6,21,9,15)(25,40,31,46,28,37,34,43)(26,41,32,47,29,38,35,44)(27,42,33,48,30,39,36,45)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)(40,41,42)(43,44,45)(46,47,48)"],rels=Vector{Int}[[1,1],[3,3,3],[-2,-3,2,3],[1,-3,1,-3],[-2,1,2,1,-2,-2],[-2,-2,-2,-2,1,-2,1,-2]],nontrivrels=Vector{Int}[[-2,-3,2,3],[1,-3,1,-3],[-2,1,2,1,-2,-2],[-2,-2,-2,-2,1,-2,1,-2]],orderdis=Tuple{Int,Int}[(1,1),(2,13),(3,2),(4,14),(6,2),(8,4),(12,4),(24,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,13),(3,1),(4,13),(6,5),(8,7),(12,5),(16,3),(24,3),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"96",aut_gens=Vector{Vector{Int}}[[[1],[2,2,2],[-3]],[[1,-2,-2],[2],[3]],[[1,3],[2],[3]],[[1],[2],[-3]],[[1],[2,2,2,2,2],[-3]]],nchars=15,dims=Int[1,1,1,1,2,2,2,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,10,12],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="D24",gens=[perm"(1,25)(2,26)(3,27)(4,28)(5,29)(6,30)(7,31)(8,32)(9,33)(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)",perm"(1,19,7,16,4,22,10,13)(2,20,8,17,5,23,11,14)(3,21,9,18,6,24,12,15)(25,37,34,46,28,40,31,43)(26,38,35,47,29,41,32,44)(27,39,36,48,30,42,33,45)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)(40,41,42)(43,44,45)(46,47,48)"],rels=Vector{Int}[[1,1],[3,3,3],[-2,1,-2,1],[-2,-3,2,3],[1,-3,1,-3],[2,2,2,2,2,2,2,2]],nontrivrels=Vector{Int}[[-2,1,-2,1],[-2,-3,2,3],[1,-3,1,-3]],orderdis=Tuple{Int,Int}[(1,1),(2,25),(3,2),(4,2),(6,2),(8,4),(12,4),(24,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,25),(3,1),(4,13),(6,9),(8,7),(12,5),(16,3),(24,3),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"192",aut_gens=Vector{Vector{Int}}[[[1],[-2],[-3]],[[1,3],[2],[3]],[[1],[2],[-3]],[[1],[-2,-2,-2],[-3]],[[1,2],[2],[-3]]],nchars=15,dims=Int[1,1,1,1,2,2,2,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,10,12],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C24.C2",gens=[perm"(1,28,4,25)(2,29,5,26)(3,30,6,27)(7,34,10,31)(8,35,11,32)(9,36,12,33)(13,40,16,37)(14,41,17,38)(15,42,18,39)(19,46,22,43)(20,47,23,44)(21,48,24,45)",perm"(1,19,7,16,4,22,10,13)(2,20,8,17,5,23,11,14)(3,21,9,18,6,24,12,15)(25,37,34,46,28,40,31,43)(26,38,35,47,29,41,32,44)(27,39,36,48,30,42,33,45)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)(40,41,42)(43,44,45)(46,47,48)"],rels=Vector{Int}[[3,3,3],[1,1,1,1],[-1,-2,1,-2],[-1,-3,1,-3],[-2,-3,2,3],[1,-2,-2,1,2,2]],nontrivrels=Vector{Int}[[-1,-2,1,-2],[-1,-3,1,-3],[-2,-3,2,3],[1,-2,-2,1,2,2]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(3,2),(4,26),(6,2),(8,4),(12,4),(24,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(3,1),(4,13),(6,1),(8,7),(12,5),(16,3),(24,3),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"192",aut_gens=Vector{Vector{Int}}[[[1],[-2],[-3]],[[1,3],[2],[3]],[[1],[2],[-3]],[[1],[2,-1,-1],[-3]],[[1,2],[2],[-3]]],nchars=15,dims=Int[1,1,1,1,2,2,2,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,2,2,1,1,2,2,2,2],galrep=Int[1,2,3,4,5,6,7,8,10,12],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*C3:C8",gens=[perm"(1,34,10,28,4,31,7,25)(2,35,11,29,5,32,8,26)(3,36,12,30,6,33,9,27)(13,46,22,40,16,43,19,37)(14,47,23,41,17,44,20,38)(15,48,24,42,18,45,21,39)",perm"(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)(25,37)(26,38)(27,39)(28,40)(29,41)(30,42)(31,43)(32,44)(33,45)(34,46)(35,47)(36,48)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)(40,41,42)(43,44,45)(46,47,48)"],rels=Vector{Int}[[2,2],[3,3,3],[-1,2,1,2],[-1,-3,1,-3],[2,-3,2,3],[1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[[-1,2,1,2],[-1,-3,1,-3],[2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(3,2),(4,4),(6,6),(8,24),(12,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(3,1),(4,3),(6,3),(8,7),(12,3),(16,3),(24,3),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"96",aut_gens=Vector{Vector{Int}}[[[1],[2],[-3]],[[1,3],[2],[3]],[[1],[2,1,1,1,1],[-3]],[[1,1,1],[2],[-3]],[[1,2],[2],[-3]]],nchars=24,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,1,1,1],galrep=Int[1,2,3,4,5,6,9,10,17,18,19,20,21,23],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C3:OD16",gens=[perm"(1,34,10,28,4,31,7,25)(2,35,11,29,5,32,8,26)(3,36,12,30,6,33,9,27)(13,46,22,40,16,43,19,37)(14,47,23,41,17,44,20,38)(15,48,24,42,18,45,21,39)",perm"(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)(25,40)(26,41)(27,42)(28,37)(29,38)(30,39)(31,46)(32,47)(33,48)(34,43)(35,44)(36,45)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)(40,41,42)(43,44,45)(46,47,48)"],rels=Vector{Int}[[2,2],[3,3,3],[-1,-3,1,-3],[2,-3,2,3],[-1,-1,-1,2,-1,2],[1,2,1,2,1,1],[-1,-1,-1,-1,2,1,2,-1]],nontrivrels=Vector{Int}[[-1,-3,1,-3],[2,-3,2,3],[-1,-1,-1,2,-1,2],[1,2,1,2,1,1],[-1,-1,-1,-1,2,1,2,-1]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(3,2),(4,4),(6,6),(8,24),(12,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(3,1),(4,3),(6,3),(8,7),(12,3),(16,3),(24,3),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"96",aut_gens=Vector{Vector{Int}}[[[1],[2,1,1,1,1],[-3]],[[1,-3],[2],[3]],[[1],[2],[-3]],[[1,1,1],[2],[-3]],[[1,2],[2],[-3]]],nchars=18,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,2,1,1,2,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,9,10,11,12,13,15],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C4*C3:C4",gens=[perm"(1,31,7,25)(2,32,8,26)(3,33,9,27)(4,34,10,28)(5,35,11,29)(6,36,12,30)(13,43,19,37)(14,44,20,38)(15,45,21,39)(16,46,22,40)(17,47,23,41)(18,48,24,42)",perm"(1,16,4,13)(2,17,5,14)(3,18,6,15)(7,22,10,19)(8,23,11,20)(9,24,12,21)(25,40,28,37)(26,41,29,38)(27,42,30,39)(31,46,34,43)(32,47,35,44)(33,48,36,45)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)(40,41,42)(43,44,45)(46,47,48)"],rels=Vector{Int}[[3,3,3],[1,1,1,1],[2,2,2,2],[-1,-2,1,2],[-1,-3,1,-3],[-2,-3,2,3]],nontrivrels=Vector{Int}[[-1,-2,1,2],[-1,-3,1,-3],[-2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(3,2),(4,28),(6,6),(12,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(3,1),(4,15),(6,3),(8,7),(12,7),(16,3),(24,3),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"192",aut_gens=Vector{Vector{Int}}[[[1,3],[2],[3]],[[-1],[2],[-3]],[[1,-2,-2],[2],[-3]],[[1],[2,-1,-1],[-3]],[[1,2],[2],[-3]]],nchars=24,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,10,12,17,18,19,20,21,23],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C6.Q8",gens=[perm"(1,28,4,25)(2,29,5,26)(3,30,6,27)(7,34,10,31)(8,35,11,32)(9,36,12,33)(13,40,16,37)(14,41,17,38)(15,42,18,39)(19,46,22,43)(20,47,23,44)(21,48,24,45)",perm"(1,19,7,13)(2,20,8,14)(3,21,9,15)(4,22,10,16)(5,23,11,17)(6,24,12,18)(25,46,31,40)(26,47,32,41)(27,48,33,42)(28,43,34,37)(29,44,35,38)(30,45,36,39)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)(40,41,42)(43,44,45)(46,47,48)"],rels=Vector{Int}[[3,3,3],[2,2,2,2],[1,1,1,1],[-1,-2,-1,2],[-1,-3,1,-3],[-2,-3,2,3]],nontrivrels=Vector{Int}[[-1,-2,-1,2],[-1,-3,1,-3],[-2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(3,2),(4,28),(6,6),(12,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(3,1),(4,15),(6,3),(8,7),(12,7),(16,3),(24,3),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"96",aut_gens=Vector{Vector{Int}}[[[1],[2,-1,-1],[-3]],[[-1],[2],[3]],[[1,-3],[2],[3]],[[1],[2],[-3]],[[1,-2,-2],[2],[-3]],[[1],[-2],[-3]]],nchars=18,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,2,2],galrep=Int[1,2,3,4,5,7,9,10,11,12,13,15,17],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C12:C4",gens=[perm"(1,31,7,25)(2,32,8,26)(3,33,9,27)(4,34,10,28)(5,35,11,29)(6,36,12,30)(13,43,19,37)(14,44,20,38)(15,45,21,39)(16,46,22,40)(17,47,23,41)(18,48,24,42)",perm"(1,16,4,13)(2,17,5,14)(3,18,6,15)(7,22,10,19)(8,23,11,20)(9,24,12,21)(25,37,28,40)(26,38,29,41)(27,39,30,42)(31,43,34,46)(32,44,35,47)(33,45,36,48)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)(40,41,42)(43,44,45)(46,47,48)"],rels=Vector{Int}[[3,3,3],[1,1,1,1],[2,2,2,2],[-1,-2,1,-2],[-1,-3,1,-3],[-2,-3,2,3]],nontrivrels=Vector{Int}[[-1,-2,1,-2],[-1,-3,1,-3],[-2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(3,2),(4,28),(6,6),(12,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(3,1),(4,15),(6,3),(8,7),(12,7),(16,3),(24,3),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"192",aut_gens=Vector{Vector{Int}}[[[1],[-2],[-3]],[[1,-3],[2],[3]],[[1],[2],[-3]],[[1],[2,-1,-1],[-3]],[[1,2],[2],[-3]]],nchars=18,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,2,2,1,1,2,1,2,1,2],galrep=Int[1,2,3,4,5,6,9,10,11,12,13,14,15,16],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="D6:C4",gens=[perm"(1,25)(2,26)(3,27)(4,28)(5,29)(6,30)(7,31)(8,32)(9,33)(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)",perm"(1,19,7,13)(2,20,8,14)(3,21,9,15)(4,22,10,16)(5,23,11,17)(6,24,12,18)(25,46,31,40)(26,47,32,41)(27,48,33,42)(28,43,34,37)(29,44,35,38)(30,45,36,39)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)(40,41,42)(43,44,45)(46,47,48)"],rels=Vector{Int}[[1,1],[3,3,3],[2,2,2,2],[-2,-3,2,3],[1,-3,1,-3],[1,2,2,1,2,2],[-2,1,2,1,-2,1,2,1]],nontrivrels=Vector{Int}[[-2,-3,2,3],[1,-3,1,-3],[1,2,2,1,2,2],[-2,1,2,1,-2,1,2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,15),(3,2),(4,16),(6,6),(12,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,15),(3,1),(4,27),(6,7),(8,7),(12,11),(16,3),(24,3),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"96",aut_gens=Vector{Vector{Int}}[[[1],[2,2,1,-2,1],[-3]],[[1,2,1,-2,1],[2],[3]],[[1,-3],[2],[3]],[[1],[2],[-3]],[[1,-2,-2],[2],[-3]],[[1],[-2],[-3]]],nchars=18,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,9,10,11,12,13,15,17],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C3:D8",gens=[perm"(1,25)(2,26)(3,27)(4,28)(5,29)(6,30)(7,31)(8,32)(9,33)(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)",perm"(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)(25,43)(26,44)(27,45)(28,46)(29,47)(30,48)(31,40)(32,41)(33,42)(34,37)(35,38)(36,39)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)(40,41,42)(43,44,45)(46,47,48)"],rels=Vector{Int}[[1,1],[2,2],[3,3,3],[1,-3,1,-3],[2,-3,2,3],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1]],nontrivrels=Vector{Int}[[1,-3,1,-3],[2,-3,2,3],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,17),(3,2),(4,2),(6,10),(8,12),(12,4)],ordersubdis=Tuple{Int,Int}[(1,1),(2,17),(3,1),(4,9),(6,9),(8,7),(12,5),(16,3),(24,3),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"96",aut_gens=Vector{Vector{Int}}[[[1],[2,1,1,2,1,2,1],[-3]],[[-2,-1,-2,-1,-1],[2],[3]],[[1,3],[2],[3]],[[1],[2],[-3]],[[1,1,2,1,2,1,2,1,2],[2],[-3]]],nchars=12,dims=Int[1,1,1,1,2,2,2,2,2,2,2,4],schur=Int[1,1,1,1,1,1,1,1,1,1,1,2],galrep=Int[1,2,3,4,5,6,7,8,10,12],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C3:SD16",gens=[perm"(1,28,4,25)(2,29,5,26)(3,30,6,27)(7,34,10,31)(8,35,11,32)(9,36,12,33)(13,40,16,37)(14,41,17,38)(15,42,18,39)(19,46,22,43)(20,47,23,44)(21,48,24,45)",perm"(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)(25,43)(26,44)(27,45)(28,46)(29,47)(30,48)(31,40)(32,41)(33,42)(34,37)(35,38)(36,39)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)(40,41,42)(43,44,45)(46,47,48)"],rels=Vector{Int}[[2,2],[3,3,3],[-1,-3,1,-3],[2,-3,2,3],[1,2,1,1,2,1],[1,2,1,2,-1,2,1,2]],nontrivrels=Vector{Int}[[-1,-3,1,-3],[2,-3,2,3],[1,2,1,1,2,1],[1,2,1,2,-1,2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,5),(3,2),(4,14),(6,10),(8,12),(12,4)],ordersubdis=Tuple{Int,Int}[(1,1),(2,5),(3,1),(4,9),(6,5),(8,7),(12,5),(16,3),(24,3),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"96",aut_gens=Vector{Vector{Int}}[[[1],[2,-1,2,-1,2],[-3]],[[1,-2,1,-2,1],[2],[3]],[[1,3],[2],[3]],[[1],[2],[-3]],[[-1],[2],[-3]]],nchars=12,dims=Int[1,1,1,1,2,2,2,2,2,2,2,4],schur=Int[1,1,1,1,1,1,1,1,1,1,1,2],galrep=Int[1,2,3,4,5,6,7,8,10,12],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="Q8:S3",gens=[perm"(1,25)(2,26)(3,27)(4,28)(5,29)(6,30)(7,31)(8,32)(9,33)(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)",perm"(1,16,4,13)(2,17,5,14)(3,18,6,15)(7,22,10,19)(8,23,11,20)(9,24,12,21)(25,46,28,43)(26,47,29,44)(27,48,30,45)(31,37,34,40)(32,38,35,41)(33,39,36,42)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)(40,41,42)(43,44,45)(46,47,48)"],rels=Vector{Int}[[1,1],[3,3,3],[-2,-3,2,3],[1,-3,1,-3],[-2,1,-2,-2,1,-2],[1,-2,1,-2,1,-2,1,2]],nontrivrels=Vector{Int}[[-2,-3,2,3],[1,-3,1,-3],[-2,1,-2,-2,1,-2],[1,-2,1,-2,1,-2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,13),(3,2),(4,6),(6,2),(8,12),(12,12)],ordersubdis=Tuple{Int,Int}[(1,1),(2,13),(3,1),(4,9),(6,5),(8,7),(12,5),(16,3),(24,3),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"96",aut_gens=Vector{Vector{Int}}[[[1],[1,-2,1,2,2],[-3]],[[1,-2,-2,-1,2,-1,2],[2],[3]],[[1,3],[2],[3]],[[1],[2],[-3]],[[1,-2,-2],[2],[-3]]],nchars=12,dims=Int[1,1,1,1,2,2,2,2,2,2,2,4],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,10,12],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C3:Q16",gens=[perm"(1,28,4,25)(2,29,5,26)(3,30,6,27)(7,34,10,31)(8,35,11,32)(9,36,12,33)(13,40,16,37)(14,41,17,38)(15,42,18,39)(19,46,22,43)(20,47,23,44)(21,48,24,45)",perm"(1,16,4,13)(2,17,5,14)(3,18,6,15)(7,22,10,19)(8,23,11,20)(9,24,12,21)(25,46,28,43)(26,47,29,44)(27,48,30,45)(31,37,34,40)(32,38,35,41)(33,39,36,42)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)(40,41,42)(43,44,45)(46,47,48)"],rels=Vector{Int}[[3,3,3],[-1,-1,2,2],[1,1,1,1],[1,1,1,1],[-1,-3,1,-3],[-2,-3,2,3],[2,-1,-2,1,-2,1,-2,-1]],nontrivrels=Vector{Int}[[-1,-1,2,2],[-1,-3,1,-3],[-2,-3,2,3],[2,-1,-2,1,-2,1,-2,-1]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(3,2),(4,18),(6,2),(8,12),(12,12)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(3,1),(4,9),(6,1),(8,7),(12,5),(16,3),(24,3),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"96",aut_gens=Vector{Vector{Int}}[[[1],[2,-1,-2,-1,2],[-3]],[[1,-2,1,2,1],[2],[3]],[[1,3],[2],[3]],[[1],[2],[-3]],[[-1],[2],[-3]]],nchars=12,dims=Int[1,1,1,1,2,2,2,2,2,2,2,4],schur=Int[1,1,1,1,1,1,1,1,1,2,2,2],galrep=Int[1,2,3,4,5,6,7,8,10,12],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C6.D4",gens=[perm"(1,31,7,25)(2,32,8,26)(3,33,9,27)(4,34,10,28)(5,35,11,29)(6,36,12,30)(13,43,19,37)(14,44,20,38)(15,45,21,39)(16,46,22,40)(17,47,23,41)(18,48,24,42)",perm"(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)(25,40)(26,41)(27,42)(28,37)(29,38)(30,39)(31,46)(32,47)(33,48)(34,43)(35,44)(36,45)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)(40,41,42)(43,44,45)(46,47,48)"],rels=Vector{Int}[[2,2],[3,3,3],[1,1,1,1],[-1,-3,1,-3],[2,-3,2,3],[2,1,1,2,1,1],[-1,2,1,2,-1,2,1,2]],nontrivrels=Vector{Int}[[-1,-3,1,-3],[2,-3,2,3],[2,1,1,2,1,1],[-1,2,1,2,-1,2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(3,2),(4,24),(6,14)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(3,1),(4,19),(6,7),(8,7),(12,11),(16,3),(24,3),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"192",aut_gens=Vector{Vector{Int}}[[[1,-3],[2],[3]],[[1],[2],[-3]],[[-1],[2],[-3]],[[1],[2,-1,-1],[-3]],[[1,2],[2],[-3]]],nchars=18,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,7,9,10,11,12,13,14,15,16],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C4*C12",gens=[perm"(1,27,3,25)(2,28,4,26)(5,31,7,29)(6,32,8,30)(9,35,11,33)(10,36,12,34)(13,39,15,37)(14,40,16,38)(17,43,19,41)(18,44,20,42)(21,47,23,45)(22,48,24,46)",perm"(1,14,2,13)(3,16,4,15)(5,18,6,17)(7,20,8,19)(9,22,10,21)(11,24,12,23)(25,38,26,37)(27,40,28,39)(29,42,30,41)(31,44,32,43)(33,46,34,45)(35,48,36,47)",perm"(1,9,5)(2,10,6)(3,11,7)(4,12,8)(13,21,17)(14,22,18)(15,23,19)(16,24,20)(25,33,29)(26,34,30)(27,35,31)(28,36,32)(37,45,41)(38,46,42)(39,47,43)(40,48,44)"],rels=Vector{Int}[[3,3,3],[1,1,1,1],[2,2,2,2],[-1,-2,1,2],[-1,-3,1,3],[-2,-3,2,3]],nontrivrels=Vector{Int}[[-1,-2,1,2],[-1,-3,1,3],[-2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(3,2),(4,12),(6,6),(12,24)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(3,1),(4,7),(6,3),(8,3),(12,7),(16,1),(24,3),(48,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"192",aut_gens=Vector{Vector{Int}}[[[1],[2],[-3]],[[1,2],[2],[-3]],[[2],[1],[-3]]],nchars=48,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,5,6,7,8,9,10,11,17,18,19,21,22,23,24,25,26,27],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C3*C2^2:C4",gens=[perm"(1,26,2,25)(3,28,4,27)(5,30,6,29)(7,32,8,31)(9,34,10,33)(11,36,12,35)(13,38,14,37)(15,40,16,39)(17,42,18,41)(19,44,20,43)(21,46,22,45)(23,48,24,47)",perm"(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)(25,39)(26,40)(27,37)(28,38)(29,43)(30,44)(31,41)(32,42)(33,47)(34,48)(35,45)(36,46)",perm"(1,9,5)(2,10,6)(3,11,7)(4,12,8)(13,21,17)(14,22,18)(15,23,19)(16,24,20)(25,33,29)(26,34,30)(27,35,31)(28,36,32)(37,45,41)(38,46,42)(39,47,43)(40,48,44)"],rels=Vector{Int}[[2,2],[3,3,3],[1,1,1,1],[-1,-3,1,3],[2,-3,2,3],[-1,2,1,1,2,-1],[-1,2,1,2,-1,2,1,2]],nontrivrels=Vector{Int}[[-1,-3,1,3],[2,-3,2,3],[-1,2,1,1,2,-1],[-1,2,1,2,-1,2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(3,2),(4,8),(6,14),(12,16)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(3,1),(4,11),(6,7),(8,3),(12,11),(16,1),(24,3),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"64",aut_gens=Vector{Vector{Int}}[[[1],[2,1,2,-1,2],[3]],[[-1],[2],[-3]],[[1],[2,-1,-1],[-3]],[[1,2],[2],[-3]]],nchars=30,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,9,10,13,14,17,18,25,26,27,28],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C3*C4:C4",gens=[perm"(1,26,2,25)(3,28,4,27)(5,30,6,29)(7,32,8,31)(9,34,10,33)(11,36,12,35)(13,38,14,37)(15,40,16,39)(17,42,18,41)(19,44,20,43)(21,46,22,45)(23,48,24,47)",perm"(1,15,3,13)(2,16,4,14)(5,19,7,17)(6,20,8,18)(9,23,11,21)(10,24,12,22)(25,37,27,39)(26,38,28,40)(29,41,31,43)(30,42,32,44)(33,45,35,47)(34,46,36,48)",perm"(1,9,5)(2,10,6)(3,11,7)(4,12,8)(13,21,17)(14,22,18)(15,23,19)(16,24,20)(25,33,29)(26,34,30)(27,35,31)(28,36,32)(37,45,41)(38,46,42)(39,47,43)(40,48,44)"],rels=Vector{Int}[[3,3,3],[2,2,2,2],[1,1,1,1],[-1,-2,1,-2],[-1,-3,1,3],[-2,-3,2,3]],nontrivrels=Vector{Int}[[-1,-2,1,-2],[-1,-3,1,3],[-2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(3,2),(4,12),(6,6),(12,24)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(3,1),(4,7),(6,3),(8,3),(12,7),(16,1),(24,3),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"64",aut_gens=Vector{Vector{Int}}[[[1],[-2],[3]],[[1],[2],[-3]],[[1],[2,-1,-1],[-3]],[[1,2],[2],[-3]]],nchars=30,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,13,15,17,19,25,26,27,29],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*C24",gens=[perm"(1,28,4,26,2,27,3,25)(5,32,8,30,6,31,7,29)(9,36,12,34,10,35,11,33)(13,40,16,38,14,39,15,37)(17,44,20,42,18,43,19,41)(21,48,24,46,22,47,23,45)",perm"(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)(25,37)(26,38)(27,39)(28,40)(29,41)(30,42)(31,43)(32,44)(33,45)(34,46)(35,47)(36,48)",perm"(1,9,5)(2,10,6)(3,11,7)(4,12,8)(13,21,17)(14,22,18)(15,23,19)(16,24,20)(25,33,29)(26,34,30)(27,35,31)(28,36,32)(37,45,41)(38,46,42)(39,47,43)(40,48,44)"],rels=Vector{Int}[[2,2],[3,3,3],[-1,2,1,2],[-1,-3,1,3],[2,-3,2,3],[1,1,1,1,1,1,1,1]],nontrivrels=Vector{Int}[[-1,2,1,2],[-1,-3,1,3],[2,-3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(3,2),(4,4),(6,6),(8,8),(12,8),(24,16)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(3,1),(4,3),(6,3),(8,3),(12,3),(16,1),(24,3),(48,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"32",aut_gens=Vector{Vector{Int}}[[[1],[2],[-3]],[[1],[2,1,1,1,1],[-3]],[[1,1,1],[2],[-3]],[[1,2],[2],[-3]]],nchars=48,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,9,10,17,18,19,20,21,22,25,26],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C3*OD16",gens=[perm"(1,28,4,26,2,27,3,25)(5,32,8,30,6,31,7,29)(9,36,12,34,10,35,11,33)(13,40,16,38,14,39,15,37)(17,44,20,42,18,43,19,41)(21,48,24,46,22,47,23,45)",perm"(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)(25,38)(26,37)(27,40)(28,39)(29,42)(30,41)(31,44)(32,43)(33,46)(34,45)(35,48)(36,47)",perm"(1,9,5)(2,10,6)(3,11,7)(4,12,8)(13,21,17)(14,22,18)(15,23,19)(16,24,20)(25,33,29)(26,34,30)(27,35,31)(28,36,32)(37,45,41)(38,46,42)(39,47,43)(40,48,44)"],rels=Vector{Int}[[2,2],[3,3,3],[-1,-3,1,3],[2,-3,2,3],[-1,-1,-1,2,-1,2],[1,2,1,2,1,1],[-1,-1,-1,-1,2,1,2,-1]],nontrivrels=Vector{Int}[[-1,-3,1,3],[2,-3,2,3],[-1,-1,-1,2,-1,2],[1,2,1,2,1,1],[-1,-1,-1,-1,2,1,2,-1]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(3,2),(4,4),(6,6),(8,8),(12,8),(24,16)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(3,1),(4,3),(6,3),(8,3),(12,3),(16,1),(24,3),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"32",aut_gens=Vector{Vector{Int}}[[[1],[2,1,1,1,1],[3]],[[1],[2],[-3]],[[1,1,1],[2],[-3]],[[1,2],[2],[-3]]],nchars=30,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,9,10,13,14,17,18,25,27],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C3*D8",gens=[perm"(1,25)(2,26)(3,27)(4,28)(5,29)(6,30)(7,31)(8,32)(9,33)(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)",perm"(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)(25,39)(26,40)(27,38)(28,37)(29,43)(30,44)(31,42)(32,41)(33,47)(34,48)(35,46)(36,45)",perm"(1,9,5)(2,10,6)(3,11,7)(4,12,8)(13,21,17)(14,22,18)(15,23,19)(16,24,20)(25,33,29)(26,34,30)(27,35,31)(28,36,32)(37,45,41)(38,46,42)(39,47,43)(40,48,44)"],rels=Vector{Int}[[1,1],[2,2],[3,3,3],[1,-3,1,3],[2,-3,2,3],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1]],nontrivrels=Vector{Int}[[1,-3,1,3],[2,-3,2,3],[2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1]],orderdis=Tuple{Int,Int}[(1,1),(2,9),(3,2),(4,2),(6,18),(8,4),(12,4),(24,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,9),(3,1),(4,5),(6,9),(8,3),(12,5),(16,1),(24,3),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"64",aut_gens=Vector{Vector{Int}}[[[1],[2,1,1,2,1,2,1],[3]],[[1,1,2,1,2,1,2,1,2],[2],[3]],[[1],[2],[-3]],[[2],[1],[-3]]],nchars=21,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,9,13,14,16,18],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C3*SD16",gens=[perm"(1,26,2,25)(3,28,4,27)(5,30,6,29)(7,32,8,31)(9,34,10,33)(11,36,12,35)(13,38,14,37)(15,40,16,39)(17,42,18,41)(19,44,20,43)(21,46,22,45)(23,48,24,47)",perm"(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)(25,39)(26,40)(27,38)(28,37)(29,43)(30,44)(31,42)(32,41)(33,47)(34,48)(35,46)(36,45)",perm"(1,9,5)(2,10,6)(3,11,7)(4,12,8)(13,21,17)(14,22,18)(15,23,19)(16,24,20)(25,33,29)(26,34,30)(27,35,31)(28,36,32)(37,45,41)(38,46,42)(39,47,43)(40,48,44)"],rels=Vector{Int}[[2,2],[3,3,3],[-1,-3,1,3],[2,-3,2,3],[1,2,1,1,2,1],[1,2,1,2,-1,2,1,2]],nontrivrels=Vector{Int}[[-1,-3,1,3],[2,-3,2,3],[1,2,1,1,2,1],[1,2,1,2,-1,2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,5),(3,2),(4,6),(6,10),(8,4),(12,12),(24,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,5),(3,1),(4,5),(6,5),(8,3),(12,5),(16,1),(24,3),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"32",aut_gens=Vector{Vector{Int}}[[[1],[2,-1,2,-1,2],[3]],[[1,-2,1,-2,1],[2],[3]],[[-1],[2],[3]],[[1],[2],[-3]]],nchars=21,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,11,13,14,16,18],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C3*Q16",gens=[perm"(1,26,2,25)(3,28,4,27)(5,30,6,29)(7,32,8,31)(9,34,10,33)(11,36,12,35)(13,38,14,37)(15,40,16,39)(17,42,18,41)(19,44,20,43)(21,46,22,45)(23,48,24,47)",perm"(1,14,2,13)(3,16,4,15)(5,18,6,17)(7,20,8,19)(9,22,10,21)(11,24,12,23)(25,40,26,39)(27,37,28,38)(29,44,30,43)(31,41,32,42)(33,48,34,47)(35,45,36,46)",perm"(1,9,5)(2,10,6)(3,11,7)(4,12,8)(13,21,17)(14,22,18)(15,23,19)(16,24,20)(25,33,29)(26,34,30)(27,35,31)(28,36,32)(37,45,41)(38,46,42)(39,47,43)(40,48,44)"],rels=Vector{Int}[[3,3,3],[-1,-1,2,2],[1,1,1,1],[1,1,1,1],[-1,-3,1,3],[-2,-3,2,3],[2,-1,-2,1,-2,1,-2,-1]],nontrivrels=Vector{Int}[[-1,-1,2,2],[-1,-3,1,3],[-2,-3,2,3],[2,-1,-2,1,-2,1,-2,-1]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(3,2),(4,10),(6,2),(8,4),(12,20),(24,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(3,1),(4,5),(6,1),(8,3),(12,5),(16,1),(24,3),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"64",aut_gens=Vector{Vector{Int}}[[[1],[2,-1,-2,-1,2],[3]],[[-1],[2],[3]],[[1],[2],[-3]],[[2],[1],[-3]]],nchars=21,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1],galrep=Int[1,2,3,4,5,6,8,11,13,14,16,18],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2.S4",gens=[perm"(1,26,2,25)(3,28,4,27)(5,30,6,29)(7,32,8,31)(9,34,10,33)(11,36,12,35)(13,38,14,37)(15,40,16,39)(17,42,18,41)(19,44,20,43)(21,46,22,45)(23,48,24,47)",perm"(1,17,9)(2,18,10)(3,19,11)(4,20,12)(5,21,13)(6,22,14)(7,23,15)(8,24,16)(25,33,41)(26,34,42)(27,35,43)(28,36,44)(29,37,45)(30,38,46)(31,39,47)(32,40,48)",perm"(1,6,2,5)(3,8,4,7)(9,11,10,12)(13,16,14,15)(17,23,18,24)(19,22,20,21)(25,28,26,27)(29,31,30,32)(33,40,34,39)(35,37,36,38)(41,45,42,46)(43,47,44,48)"],rels=Vector{Int}[[2,2,2],[-1,-1,-3,-3],[-1,-1,3,3],[-1,-2,1,-2],[-2,3,1,-2,-3,1],[2,-3,-2,-3,1,-3,1],[-3,-1,-3,1,3,-1,-3,1]],nontrivrels=Vector{Int}[[-1,-1,-3,-3],[-1,-1,3,3],[-1,-2,1,-2],[-2,3,1,-2,-3,1],[2,-3,-2,-3,1,-3,1],[-3,-1,-3,1,3,-1,-3,1]],orderdis=Tuple{Int,Int}[(1,1),(2,1),(3,8),(4,18),(6,8),(8,12)],ordersubdis=Tuple{Int,Int}[(1,1),(2,1),(3,4),(4,9),(6,4),(8,7),(12,4),(16,3),(24,1),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"48",aut_gens=Vector{Vector{Int}}[[[1],[-2],[-1,3,1]],[[1,2],[2],[3,-1,-3,1]],[[1,3,-1,3,1],[-1,-3,1,2],[3]],[[-1],[2],[3]]],nchars=8,dims=Int[1,1,2,2,2,3,3,4],schur=Int[1,1,1,2,2,1,1,2],galrep=Int[1,2,3,4,6,7,8],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="GL(2,3)",gens=[perm"(1,25)(2,26)(3,27)(4,28)(5,29)(6,30)(7,31)(8,32)(9,33)(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)",perm"(1,17,9)(2,18,10)(3,19,11)(4,20,12)(5,21,13)(6,22,14)(7,23,15)(8,24,16)(25,33,41)(26,34,42)(27,35,43)(28,36,44)(29,37,45)(30,38,46)(31,39,47)(32,40,48)",perm"(1,4,2,3)(5,7,6,8)(9,16,10,15)(11,13,12,14)(17,21,18,22)(19,23,20,24)(25,30,26,29)(27,32,28,31)(33,35,34,36)(37,40,38,39)(41,47,42,48)(43,46,44,45)"],rels=Vector{Int}[[1,1],[2,2,2],[3,3,3,3],[-2,1,-2,1],[-3,-2,3,3,2,-3],[-2,1,3,1,2,3],[-3,-2,3,-2,-3,-2]],nontrivrels=Vector{Int}[[-2,1,-2,1],[-3,-2,3,3,2,-3],[-2,1,3,1,2,3],[-3,-2,3,-2,-3,-2]],orderdis=Tuple{Int,Int}[(1,1),(2,13),(3,8),(4,6),(6,8),(8,12)],ordersubdis=Tuple{Int,Int}[(1,1),(2,13),(3,4),(4,9),(6,12),(8,7),(12,4),(16,3),(24,1),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"48",aut_gens=Vector{Vector{Int}}[[[1],[-2],[2,3,3,3,-2]],[[1,2],[2],[2,-3,-3,-3,-2]],[[1,2,3,3,3,-2,3],[-3,2],[-3]],[[1,2,-3,-3,-3,-3,-3,-3,-2],[2],[3]]],nchars=8,dims=Int[1,1,2,2,2,3,3,4],schur=Int[1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,6,7,8],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="A4:C4",gens=[perm"(1,37,13,25)(2,38,14,26)(3,39,15,27)(4,40,16,28)(5,41,17,29)(6,42,18,30)(7,43,19,31)(8,44,20,32)(9,45,21,33)(10,46,22,34)(11,47,23,35)(12,48,24,36)",perm"(1,9,5)(2,10,6)(3,11,7)(4,12,8)(13,21,17)(14,22,18)(15,23,19)(16,24,20)(25,29,33)(26,30,34)(27,31,35)(28,32,36)(37,41,45)(38,42,46)(39,43,47)(40,44,48)",perm"(1,2)(3,4)(5,8)(6,7)(9,11)(10,12)(13,14)(15,16)(17,20)(18,19)(21,23)(22,24)(25,27)(26,28)(29,30)(31,32)(33,36)(34,35)(37,39)(38,40)(41,42)(43,44)(45,48)(46,47)"],rels=Vector{Int}[[3,3],[2,2,2],[1,1,1,1],[-1,-2,1,-2],[1,1,3,-1,-1,3],[-2,-1,3,1,2,3],[2,1,3,2,3,-1,3]],nontrivrels=Vector{Int}[[-1,-2,1,-2],[1,1,3,-1,-1,3],[-2,-1,3,1,2,3],[2,1,3,2,3,-1,3]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(3,8),(4,24),(6,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(3,4),(4,19),(6,4),(8,7),(12,5),(16,3),(24,1),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"48",aut_gens=Vector{Vector{Int}}[[[1],[-2],[1,3,-1]],[[1,2],[2],[1,3,-1]],[[1],[2,3],[3]],[[-1],[-2],[1,3,-1]]],nchars=10,dims=Int[1,1,1,1,2,2,3,3,3,3],schur=Int[1,1,1,1,2,1,1,1,1,1],galrep=Int[1,2,3,5,6,7,8,9],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C4*A4",gens=[perm"(1,29,5,25)(2,30,6,26)(3,31,7,27)(4,32,8,28)(9,37,13,33)(10,38,14,34)(11,39,15,35)(12,40,16,36)(17,45,21,41)(18,46,22,42)(19,47,23,43)(20,48,24,44)",perm"(1,17,9)(2,18,10)(3,19,11)(4,20,12)(5,21,13)(6,22,14)(7,23,15)(8,24,16)(25,41,33)(26,42,34)(27,43,35)(28,44,36)(29,45,37)(30,46,38)(31,47,39)(32,48,40)",perm"(1,3)(2,4)(5,7)(6,8)(9,10)(11,12)(13,14)(15,16)(17,20)(18,19)(21,24)(22,23)(25,27)(26,28)(29,31)(30,32)(33,34)(35,36)(37,38)(39,40)(41,44)(42,43)(45,48)(46,47)"],rels=Vector{Int}[[3,3],[2,2,2],[1,1,1,1],[-1,-2,1,2],[-1,3,1,3],[3,-2,3,-2,3,-2]],nontrivrels=Vector{Int}[[-1,-2,1,2],[-1,3,1,3],[3,-2,3,-2,3,-2]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(3,8),(4,8),(6,8),(12,16)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(3,4),(4,11),(6,4),(8,7),(12,5),(16,1),(24,1),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"48",aut_gens=Vector{Vector{Int}}[[[1],[2],[-2,3,2]],[[1],[3,2],[3]],[[1],[-2],[-2,3,2]],[[-1],[-2],[-2,3,2]]],nchars=16,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,3,3,3,3],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,7,9,13,14,15],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*SL(2,3)",gens=[perm"(1,25)(2,26)(3,27)(4,28)(5,29)(6,30)(7,31)(8,32)(9,33)(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)",perm"(1,17,9)(2,18,10)(3,19,11)(4,20,12)(5,21,13)(6,22,14)(7,23,15)(8,24,16)(25,41,33)(26,42,34)(27,43,35)(28,44,36)(29,45,37)(30,46,38)(31,47,39)(32,48,40)",perm"(1,4,2,3)(5,7,6,8)(9,16,10,15)(11,13,12,14)(17,22,18,21)(19,24,20,23)(25,28,26,27)(29,31,30,32)(33,40,34,39)(35,37,36,38)(41,46,42,45)(43,48,44,47)"],rels=Vector{Int}[[1,1],[2,2,2],[-3,1,3,1],[3,3,3,3],[-2,1,2,1],[3,-2,-3,-3,2,3],[-3,-2,3,-2,3,-2]],nontrivrels=Vector{Int}[[-3,1,3,1],[-2,1,2,1],[3,-2,-3,-3,2,3],[-3,-2,3,-2,3,-2]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(3,8),(4,12),(6,24)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(3,4),(4,7),(6,12),(8,7),(12,4),(16,1),(24,1),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"48",aut_gens=Vector{Vector{Int}}[[[1],[2],[2,-3,-3,-3,-2]],[[1],[2,3],[-3]],[[1,2,3,3,3,3,3,3,-2],[2],[3]],[[1],[-2],[2,3,3,3,-2]]],nchars=14,dims=Int[1,1,1,1,1,1,2,2,2,2,2,2,3,3],schur=Int[1,1,1,1,1,1,2,2,1,1,1,1,1,1],galrep=Int[1,2,3,5,7,8,9,11,13,14],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="SL(2,3):C2",gens=[perm"(1,26,2,25)(3,28,4,27)(5,30,6,29)(7,32,8,31)(9,34,10,33)(11,36,12,35)(13,38,14,37)(15,40,16,39)(17,42,18,41)(19,44,20,43)(21,46,22,45)(23,48,24,47)",perm"(1,17,9)(2,18,10)(3,19,11)(4,20,12)(5,21,13)(6,22,14)(7,23,15)(8,24,16)(25,41,33)(26,42,34)(27,43,35)(28,44,36)(29,45,37)(30,46,38)(31,47,39)(32,48,40)",perm"(1,6,2,5)(3,8,4,7)(9,12,10,11)(13,15,14,16)(17,24,18,23)(19,21,20,22)(25,30,26,29)(27,32,28,31)(33,36,34,35)(37,39,38,40)(41,48,42,47)(43,45,44,46)"],rels=Vector{Int}[[2,2,2],[-1,-3,1,3],[-1,3,-1,3],[-3,-1,-3,-1],[-1,-2,1,2],[-3,2,-3,-3,-2,-3],[-3,-2,-3,-2,-3,-2]],nontrivrels=Vector{Int}[[-1,-3,1,3],[-1,3,-1,3],[-3,-1,-3,-1],[-1,-2,1,2],[-3,2,-3,-3,-2,-3],[-3,-2,-3,-2,-3,-2]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(3,8),(4,8),(6,8),(12,16)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(3,4),(4,7),(6,4),(8,7),(12,4),(16,1),(24,1),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"48",aut_gens=Vector{Vector{Int}}[[[1],[2],[3,-2,3,2]],[[1],[3,2],[-3]],[[-1],[2],[3]],[[1],[-2],[-2,-3,2]]],nchars=14,dims=Int[1,1,1,1,1,1,2,2,2,2,2,2,3,3],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,7,9,13,14],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*C3:Q8",gens=[perm"(1,28,4,25)(2,29,5,26)(3,30,6,27)(7,34,10,31)(8,35,11,32)(9,36,12,33)(13,40,16,37)(14,41,17,38)(15,42,18,39)(19,46,22,43)(20,47,23,44)(21,48,24,45)",perm"(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)(25,37)(26,38)(27,39)(28,40)(29,41)(30,42)(31,43)(32,44)(33,45)(34,46)(35,47)(36,48)",perm"(1,10,4,7)(2,11,5,8)(3,12,6,9)(13,22,16,19)(14,23,17,20)(15,24,18,21)(25,31,28,34)(26,32,29,35)(27,33,30,36)(37,43,40,46)(38,44,41,47)(39,45,42,48)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)(40,41,42)(43,44,45)(46,47,48)"],rels=Vector{Int}[[2,2],[4,4,4],[-1,-1,-3,-3],[-1,-3,1,-3],[-1,-1,3,3],[-1,2,1,2],[2,-3,2,3],[-1,-4,1,-4],[2,-4,2,4],[-3,-4,3,4]],nontrivrels=Vector{Int}[[-1,-1,-3,-3],[-1,-3,1,-3],[-1,-1,3,3],[-1,2,1,2],[2,-3,2,3],[-1,-4,1,-4],[2,-4,2,4],[-3,-4,3,4]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(3,2),(4,28),(6,6),(12,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(3,1),(4,15),(6,3),(8,19),(12,7),(16,3),(24,7),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"384",aut_gens=Vector{Vector{Int}}[[[1,-4],[2],[3],[4]],[[1],[2],[3],[-4]],[[1],[2,-1,-1],[3],[-4]],[[1],[2],[2,3],[-4]],[[1,3],[2],[3],[-4]]],nchars=18,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,2,1,2,1,2,2,2,2],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*C4*S3",gens=[perm"(1,25)(2,26)(3,27)(4,28)(5,29)(6,30)(7,31)(8,32)(9,33)(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)",perm"(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)(25,37)(26,38)(27,39)(28,40)(29,41)(30,42)(31,43)(32,44)(33,45)(34,46)(35,47)(36,48)",perm"(1,10,4,7)(2,11,5,8)(3,12,6,9)(13,22,16,19)(14,23,17,20)(15,24,18,21)(25,34,28,31)(26,35,29,32)(27,36,30,33)(37,46,40,43)(38,47,41,44)(39,48,42,45)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)(40,41,42)(43,44,45)(46,47,48)"],rels=Vector{Int}[[1,1],[2,2],[4,4,4],[3,3,3,3],[1,2,1,2],[1,-3,1,3],[2,-3,2,3],[1,-4,1,-4],[2,-4,2,4],[-3,-4,3,4]],nontrivrels=Vector{Int}[[1,2,1,2],[1,-3,1,3],[2,-3,2,3],[1,-4,1,-4],[2,-4,2,4],[-3,-4,3,4]],orderdis=Tuple{Int,Int}[(1,1),(2,15),(3,2),(4,16),(6,6),(12,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,15),(3,1),(4,27),(6,7),(8,19),(12,11),(16,3),(24,7),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"192",aut_gens=Vector{Vector{Int}}[[[1],[2],[3],[-4]],[[1,4],[2],[3],[4]],[[1],[2,-3,-3],[3],[-4]],[[1,2],[2],[3],[-4]],[[1],[2],[2,3],[-4]]],nchars=24,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,17,18,19,20,21,22],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*D12",gens=[perm"(1,25)(2,26)(3,27)(4,28)(5,29)(6,30)(7,31)(8,32)(9,33)(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)",perm"(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)(25,37)(26,38)(27,39)(28,40)(29,41)(30,42)(31,43)(32,44)(33,45)(34,46)(35,47)(36,48)",perm"(1,10,4,7)(2,11,5,8)(3,12,6,9)(13,22,16,19)(14,23,17,20)(15,24,18,21)(25,31,28,34)(26,32,29,35)(27,33,30,36)(37,43,40,46)(38,44,41,47)(39,45,42,48)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)(40,41,42)(43,44,45)(46,47,48)"],rels=Vector{Int}[[1,1],[2,2],[4,4,4],[3,3,3,3],[1,2,1,2],[1,-3,1,-3],[2,-3,2,3],[1,-4,1,-4],[2,-4,2,4],[-3,-4,3,4]],nontrivrels=Vector{Int}[[1,2,1,2],[1,-3,1,-3],[2,-3,2,3],[1,-4,1,-4],[2,-4,2,4],[-3,-4,3,4]],orderdis=Tuple{Int,Int}[(1,1),(2,27),(3,2),(4,4),(6,6),(12,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,27),(3,1),(4,39),(6,11),(8,19),(12,15),(16,3),(24,7),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"384",aut_gens=Vector{Vector{Int}}[[[1,-4],[2],[3],[4]],[[1],[2],[3],[-4]],[[1],[2,-3,-3],[3],[-4]],[[1],[2],[2,3],[-4]],[[1,3],[2],[3],[-4]]],nchars=18,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="D12:C2",gens=[perm"(1,25)(2,26)(3,27)(4,28)(5,29)(6,30)(7,31)(8,32)(9,33)(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)",perm"(1,16,4,13)(2,17,5,14)(3,18,6,15)(7,22,10,19)(8,23,11,20)(9,24,12,21)(25,40,28,37)(26,41,29,38)(27,42,30,39)(31,46,34,43)(32,47,35,44)(33,48,36,45)",perm"(1,7)(2,8)(3,9)(4,10)(5,11)(6,12)(13,19)(14,20)(15,21)(16,22)(17,23)(18,24)(25,34)(26,35)(27,36)(28,31)(29,32)(30,33)(37,46)(38,47)(39,48)(40,43)(41,44)(42,45)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)(40,41,42)(43,44,45)(46,47,48)"],rels=Vector{Int}[[1,1],[3,3],[4,4,4],[2,2,2,2],[-2,1,2,1],[-2,3,2,3],[-2,-4,2,4],[1,-4,1,-4],[3,-4,3,4],[2,2,3,1,3,1]],nontrivrels=Vector{Int}[[-2,1,2,1],[-2,3,2,3],[-2,-4,2,4],[1,-4,1,-4],[3,-4,3,4],[2,2,3,1,3,1]],orderdis=Tuple{Int,Int}[(1,1),(2,15),(3,2),(4,16),(6,6),(12,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,15),(3,1),(4,15),(6,7),(8,19),(12,7),(16,3),(24,7),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"96",aut_gens=Vector{Vector{Int}}[[[1],[2],[3,-2,-2],[-4]],[[1,-4],[2],[3],[4]],[[1],[2],[3],[-4]],[[1],[-2],[3],[-4]],[[1,2,3],[2],[3],[-4]]],nchars=18,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,13,15],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="S3*D4",gens=[perm"(1,25)(2,26)(3,27)(4,28)(5,29)(6,30)(7,31)(8,32)(9,33)(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)",perm"(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)(25,37)(26,38)(27,39)(28,40)(29,41)(30,42)(31,43)(32,44)(33,45)(34,46)(35,47)(36,48)",perm"(1,7)(2,8)(3,9)(4,10)(5,11)(6,12)(13,22)(14,23)(15,24)(16,19)(17,20)(18,21)(25,31)(26,32)(27,33)(28,34)(29,35)(30,36)(37,46)(38,47)(39,48)(40,43)(41,44)(42,45)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)(40,41,42)(43,44,45)(46,47,48)"],rels=Vector{Int}[[1,1],[2,2],[3,3],[4,4,4],[2,-4,2,4],[1,2,1,2],[1,3,1,3],[3,-4,3,4],[1,-4,1,-4],[2,3,2,3,2,3,2,3]],nontrivrels=Vector{Int}[[2,-4,2,4],[1,2,1,2],[1,3,1,3],[3,-4,3,4],[1,-4,1,-4],[2,3,2,3,2,3,2,3]],orderdis=Tuple{Int,Int}[(1,1),(2,23),(3,2),(4,8),(6,10),(12,4)],ordersubdis=Tuple{Int,Int}[(1,1),(2,23),(3,1),(4,39),(6,11),(8,19),(12,15),(16,3),(24,7),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"96",aut_gens=Vector{Vector{Int}}[[[1],[2],[3],[-4]],[[1],[2],[3,2,3,2,3],[4]],[[1,-4],[2],[3],[4]],[[1,2,3,2,3],[2],[3],[-4]],[[1],[3],[2],[-4]]],nchars=15,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2,4],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="D4:S3",gens=[perm"(1,25)(2,26)(3,27)(4,28)(5,29)(6,30)(7,31)(8,32)(9,33)(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)",perm"(1,16,4,13)(2,17,5,14)(3,18,6,15)(7,22,10,19)(8,23,11,20)(9,24,12,21)(25,40,28,37)(26,41,29,38)(27,42,30,39)(31,46,34,43)(32,47,35,44)(33,48,36,45)",perm"(1,7)(2,8)(3,9)(4,10)(5,11)(6,12)(13,22)(14,23)(15,24)(16,19)(17,20)(18,21)(25,34)(26,35)(27,36)(28,31)(29,32)(30,33)(37,43)(38,44)(39,45)(40,46)(41,47)(42,48)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)(40,41,42)(43,44,45)(46,47,48)"],rels=Vector{Int}[[1,1],[3,3],[4,4,4],[2,2,2,2],[-2,1,2,1],[-2,3,-2,3],[-2,-4,2,4],[1,-4,1,-4],[3,-4,3,4],[-2,3,2,1,3,1]],nontrivrels=Vector{Int}[[-2,1,2,1],[-2,3,-2,3],[-2,-4,2,4],[1,-4,1,-4],[3,-4,3,4],[-2,3,2,1,3,1]],orderdis=Tuple{Int,Int}[(1,1),(2,11),(3,2),(4,20),(6,10),(12,4)],ordersubdis=Tuple{Int,Int}[(1,1),(2,11),(3,1),(4,15),(6,7),(8,19),(12,7),(16,3),(24,7),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"96",aut_gens=Vector{Vector{Int}}[[[1],[2],[3,-2,-2],[-4]],[[1,-2,-2],[-2],[3],[4]],[[1,-4],[2],[3],[4]],[[1,-2,-2],[2],[3],[-4]],[[1],[2],[2,3],[-4]]],nchars=15,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2,4],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,2],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,13,15],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="S3*Q8",gens=[perm"(1,25)(2,26)(3,27)(4,28)(5,29)(6,30)(7,31)(8,32)(9,33)(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)",perm"(1,16,4,13)(2,17,5,14)(3,18,6,15)(7,22,10,19)(8,23,11,20)(9,24,12,21)(25,40,28,37)(26,41,29,38)(27,42,30,39)(31,46,34,43)(32,47,35,44)(33,48,36,45)",perm"(1,10,4,7)(2,11,5,8)(3,12,6,9)(13,19,16,22)(14,20,17,23)(15,21,18,24)(25,34,28,31)(26,35,29,32)(27,36,30,33)(37,43,40,46)(38,44,41,47)(39,45,42,48)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)(40,41,42)(43,44,45)(46,47,48)"],rels=Vector{Int}[[1,1],[4,4,4],[-2,-2,-3,-3],[-2,-3,2,-3],[-2,-2,3,3],[-2,1,2,1],[1,-3,1,3],[-2,-4,2,4],[1,-4,1,-4],[-3,-4,3,4]],nontrivrels=Vector{Int}[[-2,-2,-3,-3],[-2,-3,2,-3],[-2,-2,3,3],[-2,1,2,1],[1,-3,1,3],[-2,-4,2,4],[1,-4,1,-4],[-3,-4,3,4]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(3,2),(4,24),(6,2),(12,12)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(3,1),(4,15),(6,3),(8,19),(12,7),(16,3),(24,7),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"288",aut_gens=Vector{Vector{Int}}[[[1],[2],[3],[-4]],[[1,-4],[2],[3],[4]],[[1,-2,-2],[2],[3],[-4]],[[1],[2,3],[3],[-4]],[[1],[2],[2,3],[-4]]],nchars=15,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2,4],schur=Int[1,1,1,1,1,1,1,1,2,2,1,1,1,1,2],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="D6.C2^2",gens=[perm"(1,25)(2,26)(3,27)(4,28)(5,29)(6,30)(7,31)(8,32)(9,33)(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)",perm"(1,16,4,13)(2,17,5,14)(3,18,6,15)(7,22,10,19)(8,23,11,20)(9,24,12,21)(25,40,28,37)(26,41,29,38)(27,42,30,39)(31,46,34,43)(32,47,35,44)(33,48,36,45)",perm"(1,10,4,7)(2,11,5,8)(3,12,6,9)(13,19,16,22)(14,20,17,23)(15,21,18,24)(25,31,28,34)(26,32,29,35)(27,33,30,36)(37,46,40,43)(38,47,41,44)(39,48,42,45)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)(40,41,42)(43,44,45)(46,47,48)"],rels=Vector{Int}[[1,1],[4,4,4],[-2,-2,-3,-3],[-2,-3,2,-3],[-2,-2,3,3],[-2,1,2,1],[1,-3,1,-3],[-2,-4,2,4],[1,-4,1,-4],[-3,-4,3,4]],nontrivrels=Vector{Int}[[-2,-2,-3,-3],[-2,-3,2,-3],[-2,-2,3,3],[-2,1,2,1],[1,-3,1,-3],[-2,-4,2,4],[1,-4,1,-4],[-3,-4,3,4]],orderdis=Tuple{Int,Int}[(1,1),(2,19),(3,2),(4,12),(6,2),(12,12)],ordersubdis=Tuple{Int,Int}[(1,1),(2,19),(3,1),(4,15),(6,7),(8,19),(12,7),(16,3),(24,7),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"288",aut_gens=Vector{Vector{Int}}[[[1],[2],[-3],[-4]],[[1,-4],[2],[3],[4]],[[1,-2,-2],[2],[3],[-4]],[[1,3],[2,3],[3],[-4]],[[1],[2],[2,3],[-4]]],nchars=15,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2,4],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,2],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,13,15],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2^2*C3:C4",gens=[perm"(1,28,4,25)(2,29,5,26)(3,30,6,27)(7,34,10,31)(8,35,11,32)(9,36,12,33)(13,40,16,37)(14,41,17,38)(15,42,18,39)(19,46,22,43)(20,47,23,44)(21,48,24,45)",perm"(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)(25,37)(26,38)(27,39)(28,40)(29,41)(30,42)(31,43)(32,44)(33,45)(34,46)(35,47)(36,48)",perm"(1,7)(2,8)(3,9)(4,10)(5,11)(6,12)(13,19)(14,20)(15,21)(16,22)(17,23)(18,24)(25,31)(26,32)(27,33)(28,34)(29,35)(30,36)(37,43)(38,44)(39,45)(40,46)(41,47)(42,48)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)(40,41,42)(43,44,45)(46,47,48)"],rels=Vector{Int}[[2,2],[3,3],[4,4,4],[1,1,1,1],[-1,2,1,2],[-1,3,1,3],[2,3,2,3],[-1,-4,1,-4],[2,-4,2,4],[3,-4,3,4]],nontrivrels=Vector{Int}[[-1,2,1,2],[-1,3,1,3],[2,3,2,3],[-1,-4,1,-4],[2,-4,2,4],[3,-4,3,4]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(3,2),(4,24),(6,14)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(3,1),(4,19),(6,7),(8,19),(12,11),(16,3),(24,7),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"1152",aut_gens=Vector{Vector{Int}}[[[1,4],[2],[3],[4]],[[1],[2,-1,-1],[3],[-4]],[[1,3],[2],[3],[-4]],[[1],[3],[2],[-4]],[[1],[2,3],[3],[-4]]],nchars=24,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,2,1,1,2],galrep=Int[1,2,3,4,5,6,7,8,9,10,13,14,17,18,19,20,21,22,23,24],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2*C3:D4",gens=[perm"(1,25)(2,26)(3,27)(4,28)(5,29)(6,30)(7,31)(8,32)(9,33)(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)",perm"(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)(25,37)(26,38)(27,39)(28,40)(29,41)(30,42)(31,43)(32,44)(33,45)(34,46)(35,47)(36,48)",perm"(1,7)(2,8)(3,9)(4,10)(5,11)(6,12)(13,19)(14,20)(15,21)(16,22)(17,23)(18,24)(25,34)(26,35)(27,36)(28,31)(29,32)(30,33)(37,46)(38,47)(39,48)(40,43)(41,44)(42,45)",perm"(1,3,2)(4,6,5)(7,9,8)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)(40,41,42)(43,44,45)(46,47,48)"],rels=Vector{Int}[[1,1],[2,2],[3,3],[4,4,4],[2,-4,2,4],[1,2,1,2],[2,3,2,3],[3,-4,3,4],[1,-4,1,-4],[1,3,1,3,1,3,1,3]],nontrivrels=Vector{Int}[[2,-4,2,4],[1,2,1,2],[2,3,2,3],[3,-4,3,4],[1,-4,1,-4],[1,3,1,3,1,3,1,3]],orderdis=Tuple{Int,Int}[(1,1),(2,19),(3,2),(4,12),(6,14)],ordersubdis=Tuple{Int,Int}[(1,1),(2,19),(3,1),(4,31),(6,11),(8,19),(12,15),(16,3),(24,7),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"192",aut_gens=Vector{Vector{Int}}[[[1],[2],[3,1,3,1,3],[-4]],[[1,-4],[2],[3],[4]],[[1],[2,1,3,1,3],[3],[-4]],[[1,2],[2],[3],[-4]],[[1],[2],[2,3],[-4]]],nchars=18,dims=Int[1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C2^2*C12",gens=[perm"(1,26,2,25)(3,28,4,27)(5,30,6,29)(7,32,8,31)(9,34,10,33)(11,36,12,35)(13,38,14,37)(15,40,16,39)(17,42,18,41)(19,44,20,43)(21,46,22,45)(23,48,24,47)",perm"(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)(25,37)(26,38)(27,39)(28,40)(29,41)(30,42)(31,43)(32,44)(33,45)(34,46)(35,47)(36,48)",perm"(1,7)(2,8)(3,9)(4,10)(5,11)(6,12)(13,19)(14,20)(15,21)(16,22)(17,23)(18,24)(25,31)(26,32)(27,33)(28,34)(29,35)(30,36)(37,43)(38,44)(39,45)(40,46)(41,47)(42,48)",perm"(1,5,3)(2,6,4)(7,11,9)(8,12,10)(13,17,15)(14,18,16)(19,23,21)(20,24,22)(25,29,27)(26,30,28)(31,35,33)(32,36,34)(37,41,39)(38,42,40)(43,47,45)(44,48,46)"],rels=Vector{Int}[[2,2],[3,3],[4,4,4],[1,1,1,1],[-1,2,1,2],[-1,3,1,3],[2,3,2,3],[-1,-4,1,4],[2,-4,2,4],[3,-4,3,4]],nontrivrels=Vector{Int}[[-1,2,1,2],[-1,3,1,3],[2,3,2,3],[-1,-4,1,4],[2,-4,2,4],[3,-4,3,4]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(3,2),(4,8),(6,14),(12,16)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(3,1),(4,11),(6,7),(8,7),(12,11),(16,1),(24,7),(48,1)],isabelian=true,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"384",aut_gens=Vector{Vector{Int}}[[[1],[2,-1,-1],[3],[-4]],[[1,2],[2],[3],[-4]],[[1],[2,3],[3],[-4]],[[1,2],[2],[2,3],[-4]]],nchars=48,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,17,18,19,20,21,22,23,24,25,26,27,28],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C6*D4",gens=[perm"(1,25)(2,26)(3,27)(4,28)(5,29)(6,30)(7,31)(8,32)(9,33)(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)",perm"(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)(25,38)(26,37)(27,40)(28,39)(29,42)(30,41)(31,44)(32,43)(33,46)(34,45)(35,48)(36,47)",perm"(1,7)(2,8)(3,9)(4,10)(5,11)(6,12)(13,19)(14,20)(15,21)(16,22)(17,23)(18,24)(25,31)(26,32)(27,33)(28,34)(29,35)(30,36)(37,43)(38,44)(39,45)(40,46)(41,47)(42,48)",perm"(1,5,3)(2,6,4)(7,11,9)(8,12,10)(13,17,15)(14,18,16)(19,23,21)(20,24,22)(25,29,27)(26,30,28)(31,35,33)(32,36,34)(37,41,39)(38,42,40)(43,47,45)(44,48,46)"],rels=Vector{Int}[[1,1],[2,2],[3,3],[4,4,4],[1,-4,1,4],[1,3,1,3],[2,3,2,3],[2,-4,2,4],[3,-4,3,4],[1,2,1,2,1,2,1,2]],nontrivrels=Vector{Int}[[1,-4,1,4],[1,3,1,3],[2,3,2,3],[2,-4,2,4],[3,-4,3,4],[1,2,1,2,1,2,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,11),(3,2),(4,4),(6,22),(12,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,11),(3,1),(4,15),(6,11),(8,7),(12,15),(16,1),(24,7),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"128",aut_gens=Vector{Vector{Int}}[[[1],[2],[3,1,2,1,2],[4]],[[1],[2],[3],[-4]],[[1,3],[2],[3],[-4]],[[2],[1],[3],[-4]]],nchars=30,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,14,15,17,20,25,26,27,28],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C6*Q8",gens=[perm"(1,26,2,25)(3,28,4,27)(5,30,6,29)(7,32,8,31)(9,34,10,33)(11,36,12,35)(13,38,14,37)(15,40,16,39)(17,42,18,41)(19,44,20,43)(21,46,22,45)(23,48,24,47)",perm"(1,14,2,13)(3,16,4,15)(5,18,6,17)(7,20,8,19)(9,22,10,21)(11,24,12,23)(25,37,26,38)(27,39,28,40)(29,41,30,42)(31,43,32,44)(33,45,34,46)(35,47,36,48)",perm"(1,7)(2,8)(3,9)(4,10)(5,11)(6,12)(13,19)(14,20)(15,21)(16,22)(17,23)(18,24)(25,31)(26,32)(27,33)(28,34)(29,35)(30,36)(37,43)(38,44)(39,45)(40,46)(41,47)(42,48)",perm"(1,5,3)(2,6,4)(7,11,9)(8,12,10)(13,17,15)(14,18,16)(19,23,21)(20,24,22)(25,29,27)(26,30,28)(31,35,33)(32,36,34)(37,41,39)(38,42,40)(43,47,45)(44,48,46)"],rels=Vector{Int}[[3,3],[4,4,4],[-1,-1,-2,-2],[-1,-2,1,-2],[-1,-1,2,2],[-1,3,1,3],[-2,3,2,3],[-1,-4,1,4],[-2,-4,2,4],[3,-4,3,4]],nontrivrels=Vector{Int}[[-1,-1,-2,-2],[-1,-2,1,-2],[-1,-1,2,2],[-1,3,1,3],[-2,3,2,3],[-1,-4,1,4],[-2,-4,2,4],[3,-4,3,4]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(3,2),(4,12),(6,6),(12,24)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(3,1),(4,7),(6,3),(8,7),(12,7),(16,1),(24,7),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"384",aut_gens=Vector{Vector{Int}}[[[1],[2],[3,-1,-1],[4]],[[1,3],[2],[3],[-4]],[[1,2],[2],[3],[-4]],[[2],[1],[3],[-4]]],nchars=30,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,25,26,27,28],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C3*D4:C2",gens=[perm"(1,25)(2,26)(3,27)(4,28)(5,29)(6,30)(7,31)(8,32)(9,33)(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)",perm"(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)(25,38)(26,37)(27,40)(28,39)(29,42)(30,41)(31,44)(32,43)(33,46)(34,45)(35,48)(36,47)",perm"(1,8,2,7)(3,10,4,9)(5,12,6,11)(13,20,14,19)(15,22,16,21)(17,24,18,23)(25,32,26,31)(27,34,28,33)(29,36,30,35)(37,44,38,43)(39,46,40,45)(41,48,42,47)",perm"(1,5,3)(2,6,4)(7,11,9)(8,12,10)(13,17,15)(14,18,16)(19,23,21)(20,24,22)(25,29,27)(26,30,28)(31,35,33)(32,36,34)(37,41,39)(38,42,40)(43,47,45)(44,48,46)"],rels=Vector{Int}[[1,1],[2,2],[4,4,4],[3,3,3,3],[1,-3,1,3],[2,-3,2,3],[1,-4,1,4],[2,-4,2,4],[-3,-4,3,4],[1,2,3,3,1,2]],nontrivrels=Vector{Int}[[1,-3,1,3],[2,-3,2,3],[1,-4,1,4],[2,-4,2,4],[-3,-4,3,4],[1,2,3,3,1,2]],orderdis=Tuple{Int,Int}[(1,1),(2,7),(3,2),(4,8),(6,14),(12,16)],ordersubdis=Tuple{Int,Int}[(1,1),(2,7),(3,1),(4,7),(6,7),(8,7),(12,7),(16,1),(24,7),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=true,autorder=big"96",aut_gens=Vector{Vector{Int}}[[[1],[2],[-3],[4]],[[2],[1],[3],[-4]],[[1,2,3],[2],[3],[4]]],nchars=30,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,9,10,11,12,16,17,18,19,25,27],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), 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(name="C2^2*A4",gens=[perm"(1,25)(2,26)(3,27)(4,28)(5,29)(6,30)(7,31)(8,32)(9,33)(10,34)(11,35)(12,36)(13,37)(14,38)(15,39)(16,40)(17,41)(18,42)(19,43)(20,44)(21,45)(22,46)(23,47)(24,48)",perm"(1,13)(2,14)(3,15)(4,16)(5,17)(6,18)(7,19)(8,20)(9,21)(10,22)(11,23)(12,24)(25,37)(26,38)(27,39)(28,40)(29,41)(30,42)(31,43)(32,44)(33,45)(34,46)(35,47)(36,48)",perm"(1,9,5)(2,10,6)(3,11,7)(4,12,8)(13,21,17)(14,22,18)(15,23,19)(16,24,20)(25,33,29)(26,34,30)(27,35,31)(28,36,32)(37,45,41)(38,46,42)(39,47,43)(40,48,44)",perm"(1,3)(2,4)(5,6)(7,8)(9,12)(10,11)(13,15)(14,16)(17,18)(19,20)(21,24)(22,23)(25,27)(26,28)(29,30)(31,32)(33,36)(34,35)(37,39)(38,40)(41,42)(43,44)(45,48)(46,47)"],rels=Vector{Int}[[1,1],[2,2],[4,4],[3,3,3],[1,2,1,2],[1,-3,1,3],[2,-3,2,3],[1,4,1,4],[2,4,2,4],[4,-3,4,-3,4,-3]],nontrivrels=Vector{Int}[[1,2,1,2],[1,-3,1,3],[2,-3,2,3],[1,4,1,4],[2,4,2,4],[4,-3,4,-3,4,-3]],orderdis=Tuple{Int,Int}[(1,1),(2,15),(3,8),(6,24)],ordersubdis=Tuple{Int,Int}[(1,1),(2,15),(3,4),(4,35),(6,12),(8,15),(12,5),(16,1),(24,3),(48,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"144",aut_gens=Vector{Vector{Int}}[[[1],[2],[3],[4,-3,4,3]],[[1],[2],[4,3],[4]],[[1],[2],[-3],[-3,4,3]],[[1,2],[2],[-3],[-3,4,3]],[[2],[1],[-3],[-3,4,3]]],nchars=16,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,3,3,3,3],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,7,8,9,13,14,15,16],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), 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(name="C3*D9",gens=[perm"(1,28)(2,29)(3,30)(4,31)(5,32)(6,33)(7,34)(8,35)(9,36)(10,37)(11,38)(12,39)(13,40)(14,41)(15,42)(16,43)(17,44)(18,45)(19,46)(20,47)(21,48)(22,49)(23,50)(24,51)(25,52)(26,53)(27,54)",perm"(1,19,10)(2,20,11)(3,21,12)(4,22,13)(5,23,14)(6,24,15)(7,25,16)(8,26,17)(9,27,18)(28,46,37)(29,47,38)(30,48,39)(31,49,40)(32,50,41)(33,51,42)(34,52,43)(35,53,44)(36,54,45)",perm"(1,8,5,2,9,6,3,7,4)(10,17,14,11,18,15,12,16,13)(19,26,23,20,27,24,21,25,22)(28,31,34,30,33,36,29,32,35)(37,40,43,39,42,45,38,41,44)(46,49,52,48,51,54,47,50,53)"],rels=Vector{Int}[[1,1],[2,2,2],[-2,1,2,1],[-2,-3,2,3],[1,-3,1,-3],[3,3,3,3,3,3,3,3,3]],nontrivrels=Vector{Int}[[-2,1,2,1],[-2,-3,2,3],[1,-3,1,-3]],orderdis=Tuple{Int,Int}[(1,1),(2,9),(3,8),(6,18),(9,18)],ordersubdis=Tuple{Int,Int}[(1,1),(2,9),(3,4),(6,12),(9,4),(18,4),(27,1),(54,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"108",aut_gens=Vector{Vector{Int}}[[[1],[2],[-3]],[[1,-3,-3,-3,-3,-3],[2],[3]],[[1],[-2],[3,3]]],nchars=18,dims=Int[1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,7,8,10,14],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), 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(name="C3:F5",gens=[perm"(1,46,16,31)(2,47,17,32)(3,48,18,33)(4,49,19,34)(5,50,20,35)(6,51,21,36)(7,52,22,37)(8,53,23,38)(9,54,24,39)(10,55,25,40)(11,56,26,41)(12,57,27,42)(13,58,28,43)(14,59,29,44)(15,60,30,45)",perm"(1,11,6)(2,12,7)(3,13,8)(4,14,9)(5,15,10)(16,26,21)(17,27,22)(18,28,23)(19,29,24)(20,30,25)(31,36,41)(32,37,42)(33,38,43)(34,39,44)(35,40,45)(46,51,56)(47,52,57)(48,53,58)(49,54,59)(50,55,60)",perm"(1,5,4,3,2)(6,10,9,8,7)(11,15,14,13,12)(16,17,18,19,20)(21,22,23,24,25)(26,27,28,29,30)(31,33,35,32,34)(36,38,40,37,39)(41,43,45,42,44)(46,49,47,50,48)(51,54,52,55,53)(56,59,57,60,58)"],rels=Vector{Int}[[2,2,2],[1,1,1,1],[-1,-2,1,-2],[-2,-3,2,3],[3,3,3,3,3],[1,-3,-1,3,3],[1,1,-3,-1,-1,-3]],nontrivrels=Vector{Int}[[-1,-2,1,-2],[-2,-3,2,3],[1,-3,-1,3,3],[1,1,-3,-1,-1,-3]],orderdis=Tuple{Int,Int}[(1,1),(2,5),(3,2),(4,30),(5,4),(6,10),(15,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,5),(3,1),(4,15),(5,1),(6,5),(10,1),(12,5),(15,1),(20,3),(30,1),(60,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"120",aut_gens=Vector{Vector{Int}}[[[1],[-2],[-3,-3]],[[1,2],[2],[3]],[[-3,1],[2],[3]],[[1],[2],[-3,-3]]],nchars=9,dims=Int[1,1,1,1,2,2,4,4,4],schur=Int[1,1,1,1,1,2,1,1,1],galrep=Int[1,2,3,5,6,7,8],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="S3*D5",gens=[perm"(1,31)(2,32)(3,33)(4,34)(5,35)(6,36)(7,37)(8,38)(9,39)(10,40)(11,41)(12,42)(13,43)(14,44)(15,45)(16,46)(17,47)(18,48)(19,49)(20,50)(21,51)(22,52)(23,53)(24,54)(25,55)(26,56)(27,57)(28,58)(29,59)(30,60)",perm"(1,16)(2,17)(3,18)(4,19)(5,20)(6,21)(7,22)(8,23)(9,24)(10,25)(11,26)(12,27)(13,28)(14,29)(15,30)(31,46)(32,47)(33,48)(34,49)(35,50)(36,51)(37,52)(38,53)(39,54)(40,55)(41,56)(42,57)(43,58)(44,59)(45,60)",perm"(1,11,6)(2,12,7)(3,13,8)(4,14,9)(5,15,10)(16,21,26)(17,22,27)(18,23,28)(19,24,29)(20,25,30)(31,41,36)(32,42,37)(33,43,38)(34,44,39)(35,45,40)(46,51,56)(47,52,57)(48,53,58)(49,54,59)(50,55,60)",perm"(1,5,4,3,2)(6,10,9,8,7)(11,15,14,13,12)(16,20,19,18,17)(21,25,24,23,22)(26,30,29,28,27)(31,32,33,34,35)(36,37,38,39,40)(41,42,43,44,45)(46,47,48,49,50)(51,52,53,54,55)(56,57,58,59,60)"],rels=Vector{Int}[[1,1],[2,2],[3,3,3],[1,2,1,2],[1,-3,1,3],[2,-3,2,-3],[1,-4,1,-4],[2,-4,2,4],[-3,-4,3,4],[4,4,4,4,4]],nontrivrels=Vector{Int}[[1,2,1,2],[1,-3,1,3],[2,-3,2,-3],[1,-4,1,-4],[2,-4,2,4],[-3,-4,3,4]],orderdis=Tuple{Int,Int}[(1,1),(2,23),(3,2),(5,4),(6,10),(10,12),(15,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,23),(3,1),(4,15),(5,1),(6,11),(10,7),(12,5),(15,1),(20,3),(30,3),(60,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"120",aut_gens=Vector{Vector{Int}}[[[1],[2],[-3],[4]],[[1],[2,3],[3],[4]],[[1,4,4],[2],[3],[4]],[[1],[2],[3],[-4,-4]]],nchars=12,dims=Int[1,1,1,1,2,2,2,2,2,2,4,4],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,11],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C5*A4",gens=[perm"(1,41,21)(2,42,22)(3,43,23)(4,44,24)(5,45,25)(6,46,26)(7,47,27)(8,48,28)(9,49,29)(10,50,30)(11,51,31)(12,52,32)(13,53,33)(14,54,34)(15,55,35)(16,56,36)(17,57,37)(18,58,38)(19,59,39)(20,60,40)",perm"(1,17,13,9,5)(2,18,14,10,6)(3,19,15,11,7)(4,20,16,12,8)(21,37,33,29,25)(22,38,34,30,26)(23,39,35,31,27)(24,40,36,32,28)(41,57,53,49,45)(42,58,54,50,46)(43,59,55,51,47)(44,60,56,52,48)",perm"(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,44)(42,43)(45,48)(46,47)(49,52)(50,51)(53,56)(54,55)(57,60)(58,59)"],rels=Vector{Int}[[3,3],[1,1,1],[-1,-2,1,2],[-2,3,2,3],[2,2,2,2,2],[3,-1,3,-1,3,-1]],nontrivrels=Vector{Int}[[-1,-2,1,2],[-2,3,2,3],[3,-1,3,-1,3,-1]],orderdis=Tuple{Int,Int}[(1,1),(2,3),(3,8),(5,4),(10,12),(15,32)],ordersubdis=Tuple{Int,Int}[(1,1),(2,3),(3,4),(4,1),(5,1),(10,3),(12,1),(15,4),(20,1),(60,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"96",aut_gens=Vector{Vector{Int}}[[[1],[2],[-1,3,1]],[[3,1],[2],[3]],[[1],[-2,-2],[3]],[[-1],[-2],[-1,3,1]]],nchars=20,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,3,3,3,3],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,4,8,16,17],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), (name="C6*D5",gens=[perm"(1,31)(2,32)(3,33)(4,34)(5,35)(6,36)(7,37)(8,38)(9,39)(10,40)(11,41)(12,42)(13,43)(14,44)(15,45)(16,46)(17,47)(18,48)(19,49)(20,50)(21,51)(22,52)(23,53)(24,54)(25,55)(26,56)(27,57)(28,58)(29,59)(30,60)",perm"(1,16)(2,17)(3,18)(4,19)(5,20)(6,21)(7,22)(8,23)(9,24)(10,25)(11,26)(12,27)(13,28)(14,29)(15,30)(31,46)(32,47)(33,48)(34,49)(35,50)(36,51)(37,52)(38,53)(39,54)(40,55)(41,56)(42,57)(43,58)(44,59)(45,60)",perm"(1,11,6)(2,12,7)(3,13,8)(4,14,9)(5,15,10)(16,26,21)(17,27,22)(18,28,23)(19,29,24)(20,30,25)(31,41,36)(32,42,37)(33,43,38)(34,44,39)(35,45,40)(46,56,51)(47,57,52)(48,58,53)(49,59,54)(50,60,55)",perm"(1,5,4,3,2)(6,10,9,8,7)(11,15,14,13,12)(16,20,19,18,17)(21,25,24,23,22)(26,30,29,28,27)(31,32,33,34,35)(36,37,38,39,40)(41,42,43,44,45)(46,47,48,49,50)(51,52,53,54,55)(56,57,58,59,60)"],rels=Vector{Int}[[1,1],[2,2],[3,3,3],[1,2,1,2],[1,-3,1,3],[2,-3,2,3],[1,-4,1,-4],[2,-4,2,4],[-3,-4,3,4],[4,4,4,4,4]],nontrivrels=Vector{Int}[[1,2,1,2],[1,-3,1,3],[2,-3,2,3],[1,-4,1,-4],[2,-4,2,4],[-3,-4,3,4]],orderdis=Tuple{Int,Int}[(1,1),(2,11),(3,2),(5,4),(6,22),(10,4),(15,8),(30,8)],ordersubdis=Tuple{Int,Int}[(1,1),(2,11),(3,1),(4,5),(5,1),(6,11),(10,3),(12,5),(15,1),(20,1),(30,3),(60,1)],isabelian=false,iscyclic=false,issolvable=true,isnilpotent=false,autorder=big"80",aut_gens=Vector{Vector{Int}}[[[1,-4],[2],[3],[4]],[[1],[2],[3],[-4,-4]],[[1],[2],[-3],[-4]],[[1,2],[2],[-3],[-4]]],nchars=24,dims=Int[1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2],schur=Int[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],galrep=Int[1,2,3,4,5,6,7,8,13,14,17,18],fields=Vector{Rational{BigInt}}[],mod=Vector{Vector{Vector{Rational{BigInt}}}}[[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]],[[[]]]]), 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