ON THE NON-SPLIT EXTENSION 22n.Sp(2n, 2)

In this paper we give some general results on the non-split extension group (G) over bar (n) = 2(2n).Sp(2n, 2), n >= 2. We then focus on the group (G) over bar (4) = 2(8.)Sp(8, 2). We construct (G) over bar (4) as a permutation group acting on 512 points. The conjugacy classes are determined using the coset analysis technique. Then we determine the inertia factor groups and Fischer matrices, which are required for the computations of the character table of (G) over bar (4) by means of Clifford-Fischer Theory. There are two inertia factor groups namely H-1 = Sp(8, 2) and H-2 = 2(7) :Sp(6, 2), the Schur multiplier and hence the character table of the corresponding covering group of H-2 were calculated. Using the information on conjugacy classes, Fischer matrices and ordinary and projective tables of H-2, we concluded that we only need to use the ordinary character table of H-2 to construct the character table of (G) over bar (4). The Fischer matrices of (G) over bar (4) are all listed in this paper. The character table of (G) over bar (4) is a 195 x 195 complex valued matrix, it has been supplied in the PhD Thesis [2] of the first author, which could be accessed online.