Dear GAP Forum,

I have the following question: Given a (finite) pc-group G of rank r, is it
possible to construct (with the help of GAP) 'the largest' group H of the
same rank, such that H/Z(H) is isomorphic to G? Here 'the largest' means
that every other group of rank r with the above property is a homomorphic
image of H.

Any suggestion (or an example or a reference) would be appreciated.

Best regards,
Primoz.