On a group of the Form 210:(U5(2):2)

Abstract

The full automorphism group U5(2):2 of the special unitary group U5(2) has a 10-dimensional absolutely irreducible module over GF(2): Hence a split extension of the form G = 210:(U5(2):2) does exist. In this paper we first determine the conjugacy classes of G using the coset analysis technique. The structures of the inertia factor groups were determined. These are the groups U5(2):2; 21+6:((31+2:8):2) and O5(2):2. We then determine the Fischer matrices and apply the Clifford-Fischer theory to com-pute the ordinary character table of G: The Fischer matrices Fi of G are all Z-valued, with sizes range between 1 and 5. The full character table of G; which is 109 x 109 C-valued matrix is available in the PhD Thesis [1] of the rst author, which could be accessed online.