Abstract
This paper is dealing with two split extensions of the form 2(8):A(9). We refer to these two groups by (G) over bar (1) and (G) over bar (2). For (G) over bar (1), the 8-dimensional G F(2)-module is in fact the deleted permutation module for A(9). We firstly determine the conjugacy classes of (G) over bar1 and (G) over bar2 using the coset analysis technique. The structures of inertia factor groups were determined for the two extensions. The inertia factor groups of (G) over bar (1) are A(9), A(8), S-7, (A(6) x 3):2 and (A(5) x A(4)):2, while the inertia factor groups of (G) over bar (2) are A(9), PSL (2, 8):3 and 2(3):GL (3, 2). We then determine the Fischer matrices for these two groups and apply the Clifford Fischer theory to compute the ordinary character tables of (G) over bar (1) and (G) over bar (2). The Fischer matrices of (G) over bar (1) and (G) over bar (2) are all integer valued, with sizes ranging from 1 to 9 and from 1 to 4 respectively. The full character tables of (G) over bar (1) and (G) over bar (2) are 84 x 84 and 40 x 40 complex valued matrices respectively.