Abstract
The sporadic simple group Fi(22) is generated by a conjugacy class D of 3510 Fischer's 3-transpositions. In Fi(22) there are 14 classes of maximal subgroups up to conjugacy as listed in the ATLAS [10] and Wilson [31]. The group E = 2(6):Sp(6)(2) is maximal subgroup of Fi(22) 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 Fi(22) of the form 2(6):S-8 which sits maximally in E. The computations were carried out using the computer algebra systems MAGMA [9] and GAP [29].