ON A GROUP OF THE FORM 37:Sp(6; 2).

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. [ABSTRACT FROM AUTHOR]