15.72 (2002)

For a fixed prime $p$ does there exist a sequence of groups $P_n$ of order $p^n$ such that the number of conjugacy classes $k(P_n)$ satisfies $\lim_{n \to \infty} \log k(P_n)/\sqrt{n} = 0$?
Note that J. M. Riedl (J. Algebra, 218 (1999), 190–215) constructed $p$-groups for which the above limit is $2 \log p$.