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

• Main Authors: Ayoub Basheer Mohammed Basheer, Jamshid Moori
• Format: Article
• Language: English
• Published: University of Isfahan 2012-12-01
• Series: International Journal of Group Theory
• Subjects: Group extensions; Dempwolff group; character table; Clifford theory; inertia groups; Fischer matrices; Schur multiplier; projective characters; covering group
• Online Access: http://www.theoryofgroups.ir/?_action=showPDF&article=1590&_ob=e7bcdc949b15b34554b46d8c59cfc1ce&fileName=full_text.pdf

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.