TITLE: Characters of p-groups
QUESTION [7 upvotes]: Berkovich mentioned the following result of Mann in his book on p-groups:
The number of nonlinear irreducible characters of given degree in a p-group is divided by p-1.
Do you know any reference for this statement? Also, I would like to ask you if a similar assertion holds for conjugacy classes.

REPLY [2 votes]: As already explained by Geoff, the number of conjugacy classes of size $>1$ is divisible by $p-1$. A reference is:  
A. Mann: Groups with few class sizes and the centralizer equality subgroup. Israel J. Math. 142(2004), 367-380. 
The result (with a proof quite similar to Geoff's) is on page 376 (after Corollary 18).