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 (PSL₂(11) × PSL₂(11)):4, 11²:(5 × 2A₅), 7²:SL₂(7), and PSL₂(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.
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Pisani et al. (2024) studied this question.
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