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11.98 (1990)

Partially Solved

Let $r$ be the number of conjugacy classes of elements in a finite (simple) group $G$.
$\qquad$ a) (R. Brauer). Find the best-possible estimate of the form $\lvert G \rvert \leqslant f(r)$.
$\qquad$ b) Is it true that $|G| \leqslant \exp(r)$?

Contributor: S. P. Strunkov

Progress

b) No, this is not true: the group $M_{22}$ has order 443520 and contains 12 conjugacy classes (T. Plunkett, Letter of May, 9, 2000).

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