The density of the strong symmetric genus values of p-groups

Let G be a finite group. The strong symmetric genus sigma(0)(G) is the minimum genus of any Riemann surface on which G acts faithfully and preserving orientation. Let p a prime, and let J(p) be the set of integers g for which there is a p-group of strong symmetric genus g. We show that the set J(p) has density zero in the set of positive integers.