I have been doing some studying and I was wondering if there was any literature regarding the conjugacy classes size in a finite nilpotent group in determining if a group is a p-group or not. It seems to be that there is not; I was wondering if anyone knew of any literature (I can not seem to locate anything through online resources and my library). If there is no literature I am curious as to why because it seems that this would be a studied question.
EDIT: To be more precise. The question is Let G be finite nilpotent group. Given the largest class size can one determine if G is of prime power order.