The primitive permutation groups of degree 2^a·3^b

Abstract.

In this paper, we give a complete classification of all finite simple groups with maximal subgroups of index n, where n = 2^a·3^b for a, b≧ 1. As a consequence, for such n, all primitive permutation groups of degree n are given. The motivation of this work comes also from a study of Cayley graphs of certain valency on a finite simple group.