gap> G:=SymmetricGroup(10);;
gap> H:=AlternatingGroup(7);;
gap> f:=GroupHomomorphismByFunction(H,G,x->x);;
gap> F:=GroupHomology(f,3);
MappingByFunction( Pcp-group with orders [ 4, 3 ], Pcp-group with orders 
[ 2, 2, 4, 3 ], function( x ) ... end )
gap> AbelianInvariants(Range(F)/Image(F));
[ 2, 2 ]

gap> Fmod2:=GroupHomology(f,3,2);;
gap> AbelianInvariants(Range(Fmod2)/Image(Fmod2));
[ 2, 2 ]
