# The Fischer-Clifford matrices of the inertia group $2^7{:}O^{-}_{6}(2)$ of a maximal subgroup $2^7{:}Sp_6(2)$ in $Sp_8(2)$

Document Type: Research Paper

Authors

1 Stellenbosch University

2 University of the Western Cape

Abstract

The subgroups of symplectic groups which fix a non-zero vector of the underlying symplectic space are called affine subgroups., 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 $2^7{:}O^{-}_{6}(2)$ of $A(4)$ of index $28$‎.

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