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

Abstract

In cite{Demp2} Dempwolff proved the existence of a group of theform $2^{5}{^{cdot}}GL(5,2)$ (a non split extension of theelementary abelian group $2^{5}$ by the general linear group$GL(5,2)$). This group is the second largest maximal subgroup of thesporadic Thompson simple group $mathrm{Th}.$ In this paper wecalculate the Fischer matrices of Dempwolff group $overline{G} =2^{5}{^{cdot}}GL(5,2).$ The theory of projective characters isinvolved and we have computed the Schur multiplier together with aprojective character table of an inertia factor group. The fullcharacter table of $overline{G}$ is then can be calculated easily.

Keywords

• Group extensions
• Dempwolff group
• character table
• Clifford theory
• inertia groups
• Fischer matrices
• Schur multiplier
• projective characters
• covering group