Conjugacy class fusion from four maximal subgroups of the Monster

TL;DR

This paper determines how conjugacy classes from specific maximal subgroups fuse into the Monster group, supporting computational data for the GAP Character Table Library using reproducible calculations.

Contribution

It provides the first detailed conjugacy class fusion data from four specific maximal subgroups of the Monster, enhancing computational resources.

Findings

Fusion data added to GAP Character Table Library

Reproducible calculations using mmgroup package

Supports further research on Monster group structure

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 $(\text{PSL}_2(11) {\times} \text{PSL}_2(11)){:}4$, $11^2{:}(5 {\times} 2\text{A}_5)$, $7^2{:}\text{SL}_2(7)$, and $\text{PSL}_2(19){:}2$. Our proofs are supported by reproducible calculations carried out using the Python package mmgroup, a computational construction of the Monster recently developed by Seysen.