On a quotient group \(7^4 : (3 \times 2S_7)\) of a \(7\)-local subgroup of the monster \(\mathbb{M}\) (Q6613025)

The monster sporadic group \(\mathbb{M}\) is the largest of the \(26\) sporadic finite simple groups. It is well established that \(\mathbb{M}\) has a maximal \(7\)-local subgroup \(H \simeq 7^{1+4}_{+}: (3 \times 2 S_{7})\) which is the normalizer \(N_{\mathbb{M}}(7B)\) of a subgroup generated by an element in the conjugacy class \(7B\) of \(\mathbb{M}\) (see the \(\mathbb{ATLAS}\)).\N\NIn the paper under review, the authors study the representations, the ordinary character table and the Fischer-Clifford matrices of the quotient \(\overline{H}=H/Z(H)\). The character table is given in full.