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 2(5) 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) over bar = 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) over bar is then can be calculated easily.