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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]

In [U. Dempwolff, On extensions of elementary abelian groups of order 25 by GL(5; 2), Rend. Sem. Mat. Univ. Padova, 48 (1972), 359 - 364.] Dempwolff proved the existence of a group of the form 25. GL(5; 2) (a non split extension of the elementary abelian group 25 by the general linear group GL(5; 2)). This group is the second largest maximal subgroup of the sporadic Thompson simple group Th: In this paper we calculate the Fischer matrices of Dempwolff group G = 25. GL(5; 2): 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 G is then can be calculated easily. [ABSTRACT FROM AUTHOR]