The Fischer–Clifford matrices and character table of the split extension 2⁶:S₈

Abstract

The sporadic simple group Fi₂₂ is generated by a conjugacy class D of 3510 Fischer's 3-transpositions. In Fi₂₂ there are 14 classes of maximal subgroups up to conjugacy as listed in the ATLAS [10] and Wilson [31]. The group E = 2⁶:Sp₆ (2) is maximal subgroup of F i₂₂ of index 694980. In the present article we compute the Fischer-Clifford matrices and hence character table of a subgroup of the smallest Fischer group Fi₂₂ of the form 2⁶:S₈ which sits maximally in E. The computations were carried out using the computer algebra systems MAGMA [9] and GAP [29].