No-one has mentioned that here are two classes of C2 x C2 in S4. They are: transiive V4 = <I, (1 2)(3 4), (1 4)(2 3), (1 3)(2 4)>
wich is a normal subgroup of S4, and intransitive V4 = <I, (1 2)(3)(4), (1)(2)(3 4), (1 2)(3 4)> which is not. [Remark: Is Klein's V4 transitive, intransitive or abstract?] John McKay === On Tue, 19 Mar 2013, William DeMeo wrote: > There's probably a nicer way, but you could do > > gap> g:=SymmetricGroup(4); > gap> ccsg:=ConjugacyClassesSubgroups(g); > gap> V:=Representative(ccsg[5]); > gap> StructureDescription(V); > "C2 x C2" > > Cheers, > William > > > -- > William DeMeo > Department of Mathematics > University of South Carolina > http://williamdemeo.wordpress.com > mobile:808-298-4874 office:803-777-7510 > > > > > On Tue, Mar 19, 2013 at 1:13 PM, Mohammad Reza Sorouhesh > <msorouh...@gmail.com> wrote: > > Dear forum, > > > > May I ask you how can I have the subgroup of S_4 which is isomorphic with > > Z_2 X Z_2. I know that the Cayley's Theorem guaranties this event. > > > > Best Wishes > > > > M.R.Sorouhesh > > _______________________________________________ > > 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 > _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
