ON THE NON-SPLIT EXTENSION GROUP 26 Sp(6,2)

ABSTRACT. In this paper we first construct the non-split extension G = 28 Sp(6,2) as a permutation group acting on 128 points. We then determine the conjugacy classes using the coset analysis technique (J. Moori, On the Groups Gt and G of the form 210:M22 and 210.M22, PhD Thesis, University of Birmingham, 1975) and [J. Moori, 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 by means of Clifford-Fischer Theory. There are two inertia factor groups namely H1 = Sp(6,2) and H2 = 25:S6, 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 H2, we concluded that we only need to use the ordinary character table of H2 to construct the character table of G. The Fischer matrices of G are all listed in this paper. The character table of G 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.