Abstract
The symplectic group Sp(6, 2) has a 14 dimensional absolutely irreducible module over F2. Hence a split extension group of the form G = 214:Sp(6, 2) does exist. In this paper we first determine the conjugacy classes of G using the coset analysis technique. The structures of inertia factor groups were determined. The inertia factor groups are Sp(6, 2), (2(1+4) x 2(2)):(S-3 x S-3), S-3 x S-6, PSL(2, 8), (((2(2) x Q(8)):3):2):2, S-3 x A(5), and 2 x S-4 x S-3. We then determine the Fischer matrices and apply the Clifford -Fischer theory to compute the ordinary character table of G. The Fischer matrices of G are all integer valued, with size ranging from 4 to 16. The full character table of G is a 186 x 186 complex valued matrix.