Abstract
In this paper we first construct the non-split extension (G) over bar = 2(6.)Sp(6, 2) as a permutation group acting on 128 points. We then determine the conjugacy classes using the coset analysis technique [J. Moon, On the Groups G(+) and (G) over bar of the form 2(10) :M-22 and 2(10) :(M) over bar (22), PhD Thesis, University of Birmingham, 1975] and [J. Moon, On certain groups associated with the smallest Fischer group, J. London Math. Soc. (2) 23 (1981), no. 1, 61-67.], inertia factor groups and Fischer matrices, which are required for the computations of the character table of (G) over bar by means of Clifford-Fischer Theory. There are two inertia factor groups namely H-1 = Sp(6, 2) and H-2 = 2(5):S-6, the Schur multiplier and hence the character table of the corresponding covering group of H-2 were calculated. Using information on conjugacy classes, Fischer matrices and ordinary and projective tables of H-2 we concluded that we only need to use the ordinary character table of H-2 to construct the character table of (G) over bar. The Fischer matrices of (G) over bar are all listed in this paper. The character table of (G) over bar is a 67 x 67 integral matrix, it has been supplied in the PhD Thesis [A. B. M. Basheer, Clifford-Fischer Theory Applied to Certain Groups Associated with Symplectic, Unitary and Thompson Groups, University of KwaZulu-Natal, Pietermaitzburg, 2012] of the first author, which could be accessed online.