Dear Michael Leithold,

I have gap 4.1 and I compute all extensions of G by a G-module M with
'Extensions'. Is there a function which returns the module M as a
subgroup of an extension F? Or at least returns M as a group?

I think there is currently only one method for `Extensions' in the
GAP 4 library and that is the method for a finite soluble group G.
For this case, I enclose below a function which returns the elementary
abelian normal subgroup of the extension F which corresponds to the
given module.

With the next GAP 4 release I will also add a similar method to the GAP
library.

Best wishes,
         Bettina Eick


##
## F is the extension of the finite soluble group G with a G-module M
##
ModuleOfExtension := function( G, F )
    local n, m;
    n := Length(Pcgs(G));
    m := Length(Pcgs(F));
    return Subgroup(F, Pcgs(F){[n+1..m]} );
end;