The depth of the maximal subgroups of Ree groups

Abstract

We determine the combinatorial and the ordinary depth of the maximal subgroups of the simple Ree groups 2G2(q). As an application of these calculations, we determine the subdegrees of primitive actions of the groups 2G2(q). We also improve an earlier estimate of Burness, Liebeck, and Shalev on the base size of” non-standard” primitive actions of 2G2(q) on the coset space of maximal subgroups from 3 to 2.