On a maximal subgroup of the Symplectic group Sp(4,4)

Abstract

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 firstly 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 Clifford-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.

Keywords

• group extensions
• symplectic group
• inertia groups
• fischer matrices
• character table