On a maximal subgroup of the Thompson simple group

Abstract

The present paper deals with a maximal subgroup of the Thompson group, namely the group $2^{1+8}_{+}{^{\cdot}}A_{9}:= \overline{G}.$ We compute its conjugacy classes using the coset analysis method, its inertia factor groups and Fischer matrices, which are required for the computations of the character table of $\overline{G}$ by means of Clifford-Fischer Theory.