Fischer matrices of Dempwolff group ۲^{۵}{^{\cdot}}GL(۵,۲)

‎In [U‎. ‎Dempwolff‎, ‎On extensions of elementary abelian groups of order ۲^{۵} by GL(۵,۲)‎, ‎Rend‎. ‎Sem‎. ‎Mat‎. ‎Univ‎. ‎Padova‎, ۴۸ (۱۹۷۲)‎ ‎۳۵۹‎ - ‎۳۶۴.] Dempwolff proved the existence of a group of the‎ ‎form ۲^{۵}{^{\cdot}}GL(۵,۲) (a non split extension of the‎ ‎elementary abelian group ۲^{۵} by the general linear group‎ ‎GL(۵,۲))‎. ‎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} =‎ ‎۲^{۵}{^{\cdot}}GL(۵,۲). 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.  

کلیدواژه ها:

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