On 2 nonsplit extension groups associated with HS and HS:2

Abstract

The group HS:2 is the full automorphism group of the Higman--Sims group HS. The groups 24.S6 and 25.S6 are maximal subgroups of HS and HS:2, respectively. The group 24.S6 is of order 11520 and 25.S6 is of order 23040 and each of them is of index 3 850 in HS and HS:2, respectively. The aim of this paper is to first construct \overline{G} = 25.S6 as a group of the form 24.S6.2 (that is, \overline{G} = G1.2) and then compute the character tables of these 2 nonsplit extension groups by using the method of Fischer--Clifford theory. We will show that the projective character tables of the inertia factor groups are not required. The Fischer--Clifford matrices of \overline{G}1 and \overline{G} are computed. These matrices together with the partial character tables of the inertia factors are used to compute the full character tables of these 2 groups. The fusion of \overline{G}1 into \overline{G} is also given.