# On a group of the form $3^{7}{:}Sp(6,2)$

Document Type : Research Paper

Authors

North-West University (Mafikeng Campus)

Abstract

‎The purpose of this paper is the determination of the inertia‎ ‎factors‎, ‎the computations of the Fischer matrices and the ordinary‎ ‎character table of the split extension $\overline{G}=‎ ‎3^{7}{:}Sp(6,2)$ by means of Clifford-Fischer Theory‎. ‎We firstly‎ ‎determine the conjugacy classes of $\overline{G}$ using the coset‎ ‎analysis method‎. ‎The determination of the inertia factor groups of‎ ‎this extension involved looking at some maximal subgroups of the‎ ‎maximal subgroups of $Sp(6,2).$ The Fischer matrices of‎ ‎$\overline{G}$ are all listed in this paper and their sizes range‎ ‎between 2 and 10‎. ‎The character table of $\overline{G},$ which is a‎ ‎$118\times 118\ \mathbb{C}$-valued matrix‎, ‎is available in the PhD‎ ‎thesis of the first author‎, ‎which could be accessed online‎.

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