Dear Jiayue, to be precise, G is isomorphic to the alternating group. You can find such an isomorphism and determine the images of the generators as follows:
gap> G := SmallGroup(12,3); <pc group of size 12 with 3 generators> gap> StructureDescription(G); "A4" gap> a4 := AlternatingGroup(4); Alt( [ 1 .. 4 ] ) gap> iso := IsomorphismGroups(G, a4); [ f1, f2, f3 ] -> [ (2,4,3), (1,3)(2,4), (1,2)(3,4) ] gap> List(GeneratorsOfGroup(G), g -> Image(iso, g)); [ (2,4,3), (1,3)(2,4), (1,2)(3,4) ] HTH, Sven On 21.12.2016 12:40, 齐嘉悦 wrote: > > Dear Forum members, > > > When I type this in GAP: > > > gap>G:=SmallGroup(12,3); > gap>GeneratorsOfGroup(G); > the result is [f1,f2,f3],but actually the group G here is AlternatingGroup(4) > and I wonder > how could I know here what f1,f2,f3 exactly means by permutations > respectively? How > could I know what are they in A4? > > > Looking forward to any reply! > > > Thanks a lot! > > > Jiayue > > > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum > _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum