On a maximal subgroup of the symplectic group Sp(8, 2).

The simple symplectic group Sp(8, 2) has 11 conugacy classes of maximal subgroups. The fourth maximal subgroup of Sp(8, 2) is a group of the form 2 10 : A 8 : = G ¯. In this paper we study this group, where we determine its conjugacy classes and character table using the coset analysis technique together with Clifford–Fischer Theory. We determined the inertia factor groups of G ¯ and there are 7 such groups having the forms: H 1 = A 8 , H 2 = 2 3 : G L (3 , 2) , H 3 = 2 4 : (S 3 × S 3) , H 4 = 2 3 : S 4 , H 5 = S 5 , H 6 = (S 3 × S 3) : 2 and H 7 = 2 × S 4. The character table of G ¯ is a 81 × 81 complex valued matrix, while the Fischer matrices are all integer valued matrices with sizes ranging from 1 to 16. [ABSTRACT FROM AUTHOR]