Abstract
The affine general linear group 2(5):GL(5, 2) of GL(6, 2) has 6 conjugacy classes of maximal subgroups. The largest maximal subgroup is a group of the form
2+(1+8):GL(4, 2) := (G) over bar.
In this paper we firstly determine the conjugacy classes of (G) over bar using the coset analysis technique. The structures of inertia factor groups were determined. These are the groups H-1 = H-6 = GL(4, 2) similar or equal to A(8), H-2 = H-3 = 2(3):GL(3, 2), H-4 = 2(+)(1+4) :GL(2, 2) and H-5 = GL(3, 2). We then determine the Fischer matrices and apply the Clifford-Fischer theory to compute the ordinary character table of (G) over bar. The Fischer matrices of (G) over bar are all listed in this paper. These matrices satisfy some additional interesting properties (Lemmas 3 and 4) comparing to the Fischer matrices of other group extensions. Using information on conjugacy classes, Fischer matrices and ordinary and projective tables of H-1, H-2, ..., H-6, we concluded that we need to use the ordinary character tables of all the inertia factor groups to construct the character table of (G) over bar. The character table of (G) over bar is a 69 x 69 complex matrix and is given here (in the format of Clifford- Fischer theory) as Table 7.