We show that if H is a finite group with a unique minimal normal subgroup N, which is not abelian, then the number of conjugacy classes of complements of N in H is strictly smaller than |N|.
Cite this article
Andrea Lucchini, Federico Menegazzo, Marta Morigi, Complements of the socle in monolithic groups. Groups Geom. Dyn. 1 (2007), no. 4, pp. 585–611DOI 10.4171/GGD/25