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14.74 (1999)

Open

Let $k(G)$ denote the number of conjugacy classes of a finite group $G$. Is it true that $k(G) \leqslant k(P_1) \cdots k(P_s)$, where $P_1, \dots, P_s$ are Sylow subgroups of $G$ such that $\lvert G \rvert = \lvert P_1 \rvert \cdots \lvert P_s \rvert$?

Contributor: L. Pyber

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