[GAP Forum] Projection for Semidirect Product

[Sopsku]

Dear forum,

I am having some difficulty understanding projections and semidirect products. 

I think I understand Projection for a Direct Product:

f:= FreeGroup("a");; a:=f.1;;
g := f/[a^4];; a:=g.1;;    ## C4
f:= FreeGroup("b");; b:=f.1;;
h := f/[b^2];; b:=h.1;;    ## C2
## form
d:=DirectProduct(h,g);
## write elements of d terms of [e_h,e_g]
p1:=Projection(d,1);
p2:=Projection(d,2);
List(Elements(d),x->[Image(p1,x),Image(p2,x)]);

Now I would like to do soemthing similar for a semidirect product group, e.g

a:=AutomorphismGroup(g);
s:=SemidirectProduct(a,g);

but now
Projection(s,1); 
fails.

Can I use the GAP Projections to do a decomposition similar to the  direct
product example above?

Thank you for any help.