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 $196883 = 47.59.71$ 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 $\mathbb M$.