On a maximal subgroup of the Conway group Co3

This paper is dealing with a split extension group of the form 3(5):(2xM(11)); which is a maximal subgroup of the Conway simple group Co-3:We refer to this extension by (G) over bar. We firstly determine the conjugacy classes of (G) over bar using the coset analysis technique. The structures of inertia factor groups were determined through deep investigation on the maximal subgroups of the maximal subgroups of 2 x M-11: We found the inertia factors to be the groups 2 x M-11, A(6)(2) (non-split) and (S-3 x S-3):(2): We then determine the Fischer matrices of (G) over bar and apply the Clifford-Fischer theory to compute the ordinary character table of this group. The Fischer matrices of (G) over bar are all integer valued, with sizes ranging from 1 to 4. The full character table of (G) over bar is 37x37 complex valued matrix and is given at the end of this paper.