Abstract
The Fischer group Fi(24) = Aut(Fi(24)') is the largest 3-transposition sporadic group of order 2510411418381323442585600 = 2(22).3(16).5(2).7(3).11.13.17.23.29. It is generated by a conjugacy class of 306936 transpositions. Wilson [15] completely determined all the maximal 3-local subgroups of Fi(24). In the present paper, we determine the Fischer-Clifford matrices and hence compute the character table of the non-split extension 3(7).(O-7(3):2), which is a maximal 3-local subgroup of the automorphism group Fi(24) of index 125168046080 using the technique of Fischer-Clifford matrices. Most of the calculations are carried out using the computer algebra systems GAP and MAGMA.