Fischer matrices of Dempwolff group $2^{5}{^{cdot}}GL(5,2)$

Abstract

‎In [U‎. ‎Dempwolff‎, ‎On extensions of elementary abelian groups of order $2^{5}$ by $GL(5,2)$‎, ‎<em>Rend‎. ‎Sem‎. ‎Mat‎. ‎Univ‎. ‎Padova</em>‎, <strong>48</strong> (1972)‎ ‎359‎ - ‎364.] Dempwolff proved the existence of a group of the‎ ‎form $2^{5}{^{cdot}}GL(5,2)$ (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 $mathrm{Th}.$ In this paper we‎ ‎calculate the Fischer matrices of Dempwolff group $overline{G} =‎ ‎2^{5}{^{cdot}}GL(5,2).$ 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 $overline{G}$ is then can be calculated easily‎. <br />