On a Group of the Form 24+5:GL(4, 2)

Abstract

Abstract. In [U. Dempwolff, On extensions of elementary abelian groups of order 25 by GL(5, 2), Rend. Sem. Mat. Univ. Padova, 48 (1972), 359 - 364.] Dempwolff proved the existence of a group of the form 2 5·GL(5, 2) (a non split extension of the elementary abelian group 25 by the general linear group GL(5, 2)). This group is the second largest maximal subgroup of the sporadic Thompson simple group Th. In this paper we calculate the Fischer matrices of Dempwolff group G = 25·GL(5, 2). The theory of projective characters is involved and we have computed the Schur multiplier together with a projective character table of an inertia factor group. The full character table of G is then can be calculated easily