The Fischer-Clifford matrices of an extension group of the form 2^7:(2^5:S_6)

Abstract

The split extension group $A(4)cong 2^7{:}Sp_6(2)$ is the affine subgroup of the symplectic group $Sp_8(2)$ of index $255$‎. ‎In this paper‎, ‎we use the technique of the Fischer-Clifford matrices to construct the character table of the inertia group $2^7{:}(2^5{:}S_{6})$ of $A(4)$ of index $63$‎.