Dear forum,
take a look at the following GAP code:
G:=AlternatingGroup(4);
N:=Subgroup(G,[(1,2)(3,4),(1,3)(2,4)]);
H:=DirectProduct(CyclicGroup(2),CyclicGroup(2));
A:=AutomorphismGroup(H);
P:=SylowSubgroup(A,3);
epi:=NaturalHomomorphismByNormalSubgroup(G,N);
iso:=IsomorphismGroups(FactorGroup(G,N),P);
f:=CompositionMapping(IsomorphismGroups(FactorGroup(G,N),P),epi);
SemidirectProduct(G,f,H);
After the command "SemidirectProduct(G,f,H);" GAP returns:
"Error, not ready yet, only finite polycyclic groups are allowed"
But every group in my example is finite polycyclic, even the semidirect
product would be. I can't imagine, what should be the problem in
constructing semidirect products.
Thanks for any help,
Benjamin
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