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.