G:=AutomorphismGroupAsCrossedModule(QuaternionGroup(8));;
Print(StructureDescription(HomotopyGroup(G,1)),"\n");
Print(StructureDescription(HomotopyGroup(G,2)),"\n");
F:=FreeGroup(2);;x:=F.1;;y:=F.2;;
Y:=F/[x^2, y^2*x*y^-1*x^-1];;
Print(CrossedInvariant(Y,G),"\n");
