Conjugacy class fusion from four maximal subgroups of the Monster

Abstract

We determine the conjugacy class fusion from certain maximal subgroups of the Monster to the Monster, to justify the addition of these data to the Character Table Library in the computational algebra system GAP. The maximal subgroups in question are $\left({\mathrm{PSL}}_2\right(11)\times {\mathrm{PSL}}_2(11\left)\right):4$, ${11}^2:(5\times 2{\text{A}}_5)$, $7^2:{\text{SL}}_2\left(7\right)$, and ${\mathrm{PSL}}_2\left(19\right):2$. Our proofs are supported by reproducible calculations carried out using the Python package mmgroup, a computational construction of the Monster recently developed by Seysen.