The automorphisms of class two groups of prime exponent

Abstract

We give a complete list of all the 70 class two groups of exponent p (p>2) and order p^k for k<9. For each of these groups the number of conjugacy classes is a polynomial in p, and the order of the automorphism group is a polynomial in p. In contrast, Marcus du Sautoy and Michael Vaughan-Lee have given an example of a class two group of exponent p and order p^9 for which neither the number of conjugacy classes, nor the order of the automorphism group is polynomial on residue classes (PORC).