Orbits classifying extensions of prime power order groups

The strong isomorphism classes of extensions of finite groups are parametrized by orbits of a prescribed action on the second cohomology group. We study these orbits in the case of extensions of a finite abelian p-group by a cyclic factor of order p. As an application, we compute the number and sizes of these orbits when the initial p-group is generated by at most ۳ elements.

Keywords:

Cohomology of finite p-groups , Group extensions , strong isomorphism , orbit sizes