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

The group HS:2 is the full automorphism group of the Higman–Sims group HS. The groups 2^4.S6 and 2^5.S6 are maximal subgroups of HS and HS:2, respectively. The group 2^4.S6 is of order 11520 and 2^5.S6 is of order 23040 and each of them is of index 3850 in HS and HS:2, respectively. The aim of this paper is to first construct G = 2^5.S6 as a group of the form 2^4.S6.2 (that is, 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 ofthe inertia factor groups are not required. The Fischer–Clifford matrices of G1 and 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 2groups. The fusion of G1 into G is also given.