Fischer-Clifford matrices and character table of the maximal subgroup \((2^9 :(L_3(4)) : 2\) of \(U_6(2) : 2\) (Q2330295)

Summary: The automorphism group \(U_6(2) : 2\) of the unitary group \(U_6(2) \cong F i_{21}\) has a maximal subgroup \(\overline{G}\) of the form \((2^9 :(L_3(4)) : 2\) of order 20643840. In this paper, Fischer-Clifford theory is applied to the split extension group \(\overline{G}\) to construct its character table. Also, class fusion from \(\overline{G}\) into the parent group \(U_6(2) : 2\) is determined.