The centralizer of an element of order 3 in the monster group is a triple cover of the sporadic simple group Fi24, as a result of which the prime 3 plays a special role in its theory.
When reduced modulo 3 this has 1-dimensional invariant subspaces and quotient spaces, giving an irreducible representation of dimension 781 over the field with 3 elements.
Conway and Norton suggested in their 1979 paper that monstrous moonshine is not limited to the monster, but that similar phenomena may be found for other groups.
Larissa Queen and others subsequently found that one can construct the expansions of many Hauptmoduln from simple combinations of dimensions of sporadic groups.
where one can set the constant term a(0) = 42 (OEIS: A030197), Linton & Wilson (1991) found the 25 conjugacy classes of maximal subgroups of Fi24' as follows: