[GAP Forum] Re: a semidirect product

[gapforum at mowsey.org]

I am not sure if this is the best method, but it appears to
work well enough. I assume Q is a given group, and then:

 A:=AutomorphismGroup(Q);
 QQ:=DirectProduct(Q,Q);

 p1:=Projection(QQ,1);
 p2:=Projection(QQ,2);
 e1:=Embedding(QQ,1);
 e2:=Embedding(QQ,2);

 L:=List(GeneratorsOfGroup(A), a->
        GroupHomomorphismByImages(QQ,QQ,
                GeneratorsOfGroup(QQ),
                List(GeneratorsOfGroup(QQ),g->
                        Image(CompositionMapping(e1,a,p1),g)*
                        Image(CompositionMapping(e2,a,p2),g))));

AA:=Group(L);
HH:=SemidirectProduct(AA,QQ);