Enumerating isoclinism classes of semi-extraspecial groups

Abstract

We enumerate the number of isoclinism classes of semi-extraspecial p-groups with derived subgroup of order p 2 . To do this, we enumerate GL(2, p)orbits of sets of irreducible, monic polynomials in Fp [x]. Along the way, we also provide a new construction of an infinite family of semi-extraspecial groups as central quotients of Heisenberg groups over local algebras.