[GAP Forum] A question on semidirect products

[Anvita]

Dear forum,

I am trying to construct in GAP the natural semidirect product 
of SL(2,4) and the underlying vector space GF(4)^2 and then
get hold of the normal elementary abelian 2-group *inside* the product.
Here is what I get.

--------------------------------------------
gap> S:=SL(2,4);
SL(2,4)
gap> V:=GF(4)^2;
( GF(2^2)^2 )
gap> SV:=SemidirectProduct(S,V);
<matrix group of size 960 with 3 generators>
gap> VV:=Image(Embedding(SV,2),V);;
gap> IsNormal(SV,VV);
false
--------------------------------------------

Why isn't VV normal in SV?

Thank you
Anvita


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