Oihana Garayalde - Matematika Saila, Euskal Herriko Unibertsitatearen Zientzia eta Teknologia Fakultatea, Posta-kutxa ۶۴۴, ۴۸۰۸۰ Bilbo, Spain
Mima Stanojkovski - Dipartimento di Matematica, Università di Trento, via Sommarive ۱۴, ۳۸۱۲۳ Povo (Trento), Italy

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.

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