On a group of the form 214:Sp(6, 2)

Abstract

The symplectic group Sp(6, 2) has a 14−dimensional absolutely irreducible module over . Hence a split extension group of the form Ḡ = 214:Sp(6, 2) does exist. In this paper we first determine the conjugacy classes of Ḡ using the coset analysis technique. The structures of inertia factor groups were determined. The inertia factor groups are Sp(6, 2), (21+4 × 22):(S3 × S3), S3 × S6, PSL(2, 8), (((22 ×Q8):3):2):2, S3 ×A5,and 2×S4 ×S3.We then determine the Fischer matrices and apply the Clifford-Fischer theory to compute the ordinary character table of . The Fischer matrices of are all integer valued, with size ranging from 4 to 16. The full character table of is a 186 × 186 complex valued matrix.