Verification of the conjugacy classes and ordinary character table of the Monster

Abstract

As part of the programme to re-compute the character tables of all the groups in the Atlas we re-compute the character table of $\mathbb{M}$, the Monster simple group. We operate under the uniqueness hypotheses of $\mathbb{M}$ and the existence of an ordinary faithful representation of degree $196883=\mathrm{47.59.71}$ and determine the conjugacy classes and centralizer orders of the elements of $\mathbb{M}$. Along the way we re-compute the character tables of centralizers of $p$-elements for $p<11$ as well as fusions of conjugacy classes of these centralizers in $\mathbb{M}$.