7.30 (1980)

The answer is known mod CFSG. For the alternating groups and groups of Lie type see (Ya. N. Nuzhin, Algebra and Logic, 36, no. 4 (1997), 245–256). For sporadic groups B. L. Abasheev, A. V. Ershov, N. S. Nevmerzhitskaya, S. Norton, Ya. N. Nuzhin, A. V. Timofeenko have shown that the groups $M_{11}$, $M_{22}$, $M_{23}$, and $McL$ cannot be generated as required, while the others can; see more details in (V. D. Mazurov, Siberian Math. J., 44, no. 1 (2003), 160–164).