Minimal permutation representations of finite simple exceptional groups of typesG 2 andF 4

Abstract

A minimal permutation representation of a group is a faithful permutation representation of least degree. Well-studied to date are the minimal permutation representations of finite sporadic and classical groups for which degrees, point stabilizers, as well as ranks, subdegrees, and double stabilizers, have been found. Here we attempt to provide a similar account for finite simple ezceptional groups of types G2 and F4.