Fischer-Clifford Matrices of the Non-Split Group Extension 2⁶˙U ₄(2)

Abstract

The Harada-Norton group HN is a sporadic simple group of order 273030912000000 equal to 2¹⁴ × 3⁶ × 5⁶ × 7 × 11 × 19. It has 14 conjugacy classes of maximal subgroups and in the present paper we construct the Fischer-Clifford matrices and hence character table for one of these maximal subgroups, that is the non-split extension 2⁶˙U ₄(2), of index 164587500. There is not that many known examples of the application of Fischer-Clifford theory to non-split extensions, and hence this maximal subgroup of Hard-Norton's group serves as a good candidate. Most of the computations were carried out using the computer algebra systems GAP and MAGMA.