The Monster is a Hurwitz group

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Twists of X(7) and primitive solutions to x^2+y^3=z^7 (2005, methodology): “Specifically, the Galois group should be a Hurwitz group: a finite group generated by elements a, b, c of orders 2, 3, 7, respectively, such that abc = 1. In principle we could use any Hurwitz group (even the monster group is a possibility [ Wilson2001 ]), but to make future computations practical, ”
Notes on Coxeter Transformations and the McKay Correspondence (2005, background): “s act in the ndimensional vector space over the ﬁeld F q of the prime characteristic q). 133 134 B. MISCELLANEOUS The sporadic groups have been treated in a series of papers by Woldar and others, see [Wi01] for a survey and references. R. A. Wilson shows in [Wi01], that the Monster is also a Hurwitz”
Characters and Automorphism Groups of Compact Riemann Surfaces (2000, background): “The Monster is a Hurwitz group. For details, see [Wil93, Wil97, Wil01 ].”
The locus of curves with prescribed automorphism group (Communications in Arithmetic Fundamental Groups) (2002, background): “In 2001, Wilson [31] showed the monster is a Hurwitz group.”