Dear Jan Draisma,
thanks for your hints. But I don't know how to make the
InverseGeneralMapping. Perhaps you can show me that by the following
example.
G:=Group([ (5,7)(6,8), (1,2), (1,5)(2,6)(3,7)(4,8), (1,3)(2,4)(5,7)(6,8),
  (3,4)(5,6), (1,2)(3,4), (1,2)(3,4)(5,6)(7,8) ])
Z0=1; 
gap> Z1:=Centre(G);
Group([ ( 1, 2)( 3, 4)( 5, 6)( 7, 8) ])
gap> hom:=NaturalHomomorphismByNormalSubgroup(G,Z1);
Pcgs([ (1,5)(2,6)(3,7)(4,8), (7,8), ( 3, 4), (1,3)(2,4), (5,8)(6,7),
(5,7)(6,8)
 ]) -> [ f1, f2, f3, f4, f5, f6 ]
gap> F:=FactorGroup(G,Z1);
<pc group of size 64 with 6 generators>
gap> C:=Centre(F);
Group([ f5*f6 ])
But how can I take the inverse Image of C ?
Best wishes
K.Ewald

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