The sporadic simple group F i22 is generated by a conjugacy class D of 3510 Fischer’s 3-transpositions. In F i22 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 F i22 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].