  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.
