gap> bhomc:=NaturalHomomorphismByNormalSubgroup(b,a);
gap> B:=TrivialGModuleAsGOuterGroup(G,b);
gap> C:=TrivialGModuleAsGOuterGroup(G,Image(bhomc));
gap> psi:=GOuterGroupHomomorphism();
gap> psi!.Source:=B;
gap> psi!.Target:=C;
gap> psi!.Mapping:=bhomc;

gap> Hpsi:=CohomologyHomomorphism(psi,3);

gap> Size(KernelOfGOuterGroupHomomorphism(Hpsi));
8
