On the inertia groups of the maximal subgroup 2⁷:Sp₆(2) in Aut(Fi₂₂)

Abstract

The group 2⁷:Sp₆(2) is a maximal subgroup of Aut(Fi₂₂) of index 694980. The group Aut(Fi₂₂) is the full automorphism group of the smallest Fischer simple group Fi₂₂. In this paper, we construct the character table of the inertia group 2⁷:(2⁵:S₆) of 2⁷:Sp₆(2) of index 63 through its Fischer-Clifford matrices. The split extension group 2⁷:(2⁵:S₆) sits maximally inside 2⁷:Sp₆(2).