Computing the conjugacy classes and character table of a non-split extension 2⁶·(2⁵:<em>S</em>₆) from a split extension 2⁶:(2⁵:<em>S</em>₆)

Abstract

In this paper, we will demonstrate how the character table of a sub-maximal subgroup $2^6{:}(2^5{:}S_6)$ of the sporadic simple group $Fi_{22}$ can be used to obtain the conjugacy classes and character table of a non-split extension of the form $2^6{{}^{\cdot}}(2^5{:}S_6)$, which sits maximal in the unique non-split extension $2^6{{}^{\cdot}}Sp_6(2)$.

Keywords

• coset analysis
• fischer-clifford matrices
• non-split extension
• inertia factor
• projective character table
• fusion map
• restriction of characters