[GAP Forum] S4 isomorphic to semi-direct product of V4 and S3

[Benjamin Sambale]

Hi Ron,

you need to take the whole automorphism group:

V:=AbelianGroup([2,2]);
A:=AutomorphismGroup(V);
G:=SemidirectProduct(A,V);
StructureDescription(G); #gives S4
StructureDescription(A); #gives S3

Best wishes,
Benjamin

Am 22.09.2013 00:38, schrieb Sopsku:
> Dear Forum,
>
> I am continuing my struggle with trying to learn GAP and group theory at the
> same time.
>
> I am looking at a problem set where it asks to show that S4 is isomorphic to
> the semi-direct product of V4 (i.e. C2xC2) and S3. I cannot seem to form
> this semi-direct product. [i.e. I cannot find elements in the
> AutomorphismGroup that match up with the order of the group in order to find
> the GroupHomomorphismbyImages as I have done for simpler examples such as A4
> isomorphic to semi-direct product of C3 and V4]
>
> How do I use GAP to form the semi-direct product S3 and V4.
>
> Thank you for your help.
>      Ron
>
>
>
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