[GAP Forum] A Subgroup of S_4 and isomorphic with Z_2 x Z_2

[John McKay]

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
> <msorouhesh at 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
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