Dear forum, gap> G:= SymmetricGroup(4); Sym( [ 1 .. 4 ] ) gap> H:= AllSubgroups(G);; gap> Length(H); 30 gap> M:= List([1..30],i->Size(H[i])); [ 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 8, 8, 8, 12, 24 ] gap> Collected(M); [ [ 1, 1 ], [ 2, 9 ], [ 3, 4 ], [ 4, 7 ], [ 6, 4 ], [ 8, 3 ], [ 12, 1 ], [ 24, 1 ] ]
gap> List([15..30],j->List([3..10],i->IsSubgroup(H[j],H[i]))); [ [ true, true, false, false, false, false, false, false ], [ false, false, true, false, false, true, false, false ], [ false, true, false, true, false, false, false, true ], [ true, false, false, false, true, false, true, false ], [ false, false, false, false, false, false, false, false], [ true, false, false, false, false, false, false, false], [ false, true, false, false, false, false, false, false ], [ false, false, true, true, true, false, false, false ], [ false, false, true, false, false, false, true, true ], [ false, false, false, true, false, true, true, false ], [ false, false, false, false, true, true, false, true ], [ true, true, true, false, false, true, false, false ], [ true, true, false, true, false, false, false, true ], [ true, true, false, false, true, false, true, false ], [ true, true, false, false, false, false, false, false ], [ true, true, true, true, true, true, true, true ] ] This is an illustration of order of subgroups in S4:(2,4),(2,6),(2,8),(2,12) and(2,24). Can someone help me to write a program that can compute for subgroup order of these pairs (2,4,24) and (2,4,8,24) in S4? Thanks Mike _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum