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17.77 (2010)

Solved

Let $k$ be a positive integer such that there is an insoluble finite group with exactly $k$ conjugacy classes. Is it true that a finite group of maximal order with exactly $k$ conjugacy classes is insoluble?

Contributor: R. Heffernan, D. MacHale

Progress

No, it is not; see Table 1 in (A. Vera-Lopez, J. Sangroniz, Math. Nachr., 280, no. 5–6 (2007), 676–694).

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