S:=SylowSubgroup(SymmetricGroup(8),2);;
N:=DerivedSubgroup(S);;
ON := GOuterGroup(S,N);;
A := Centre(ON);;
G:=ActingGroup(A);;
Print(StructureDescription(G),"\n");
Print(StructureDescription(N),"\n");
R:=ResolutionFiniteGroup(G,3);;
C:=HomToGModule(R,A);;
CH:=CohomologyModule(C,2);;
Elts:=Elements(ActedGroup(CH));;
lst:=List(Elts{[1..Length(Elts)]}, x->CH!.representativeCocycle(x));;
EXT:=List(lst, x->CcGroup(ON, x));;
Print(List(EXT,IdGroup),"\n");
ch:=ActedGroup(CH);;
cocycle2:=CH!.representativeCocycle(Elements(ch)[2]);
Print(cocycle2,"\n");
cocycle3:=CH!.representativeCocycle(Elements(ch)[3]);
Print(cocycle3,"\n");
class2:=CohomologyClass(CH,cocycle2);
Print(class2,"\n");
class3:=CohomologyClass(CH,cocycle3);
Print(class3,"\n");
Print(class2=class3,"\n");
