On a group of the form 37: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 G¯¯¯¯=‎‎37:Sp(6,2) by means of Clifford-Fischer Theory‎. ‎We firstly‎ ‎determine the conjugacy classes of 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 ‎G¯¯¯¯ are all listed in this paper and their sizes range‎ ‎between 2 and 10‎. ‎The character table of G¯¯¯¯, which is a‎ ‎118×118 C-valued matrix‎, ‎is available in the PhD‎ ‎thesis of the first author‎, ‎which could be accessed online‎.