This paper is dealing with a split extension group of the form 26: (3,A5),which is the largest maximal subgroup of the Symplectic group Sp(4,4): We refer to this extension by G: We , rstly determine the conjugacy classes of G using the coset analysis technique. The structures of inertia factor groups were determined. We then compute the Fischer matrices of G and apply the Cli , ord-Fischer theory to calculate the ordinary character table of this group. The Fischer matrices of G are all integer valued, with sizes ranging from 1 to 4. The full character table of G is 26, 26 complex valued matrix and is given at the end of this paper.