CONSTRUCTION OF A 45,694-DIMENSIONAL SIMPLE MODULE OF LYONS SPORADIC GROUP OVER GF(2)

It is shown that the e-modular reduction phi of the smallest nontrivia l, rational, absolutely irreducible character chi of Lyons' sporadic s imple group Ly is irreducible. Furthermore, an explicit 45,694-dimensi onal irreducible matrix representation of Ly over the field GF(2) with two elements is given. The construction has been performed on a paral lel computer of type IBM SP1 with 10 nodes. It uses the recent present ation of Ly as a permutation group on 9,606,125 points given by Cooper man, Finkelstein, Tselman, and York. (C) Elsevier Science Inc., 1997.