FISCHER MATRICES OF DEMPWOLFF GROUP 25.GL(5; 2)

Abstract. In [U. Dempwolff, On extensions of elementary abelian groups of order 2^5 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 = 2^5.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.