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

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 firstly‎‎determine 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 ‎$118times 118 mathbb{C}$-valued matrix‎, ‎is available in the PhD‎ ‎thesis of the first author‎, ‎which could be accessed online‎.

Keywords

• Group extensions
• symplectic group
• character table
• inertia groups
• Fischer matrices