On a group extension involving the Suzuki group Sz(8)

The Suzuki simple group Sz(8) has an automorphism group 3. Using the electronic Atlas [22], the group Sz(8) : 3 has an absolutely irreducible module of dimension 12 over F-2. Therefore a split extension group of the form 2(12):(Sz(8):3):=G exists. 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 by analysing the maximal subgroups of Sz(8) : 3 and maximal of the maximal subgroups of Sz(8) : 3 together with various other information. It turns out that the character table of G is a 43x43 complex valued matrix, while the Fischer matrices are all integer valued matrices with sizes ranging from 1 to 7.