THE FISCHER-CLIFFORD MATRICES OF THE GROUP 2⁶: SP ₆(2)

Abstract

The smallest Fischer sporadic simple group F₂₂ has 14 maximal subgroups up to conjugacy as listed in [2] and [15]. The group 2⁶: SP ₆(2) is a maximal subgroup of F ₂₂ of index 694980. We use the technique of the Fischer-Clifford matrices to constuct the character table of the group 2⁶: SP ₆(2). The Fischer-Clifford matrices of 2⁶: SP ₆(2) are used, together with the character tables of SP ₆(2) and a maximal subgroup 2⁵:S ₆ SP ₆ (2) of index 63, to construct the character table of 2⁶: SP ₆ (2).