The character tables of centralizers in Sporadic Simple Groups of ${\rm McL}$

TL;DR

This paper computes the conjugacy class representatives and character tables of centralizers in the McL sporadic simple group using GAP to aid in classifying finite dimensional pointed Hopf algebras.

Contribution

It provides the first complete set of character tables for centralizers in McL, facilitating further algebraic classification work.

Findings

Conjugacy class representatives of McL identified.

Character tables of all centralizers computed.

Results support classification of related Hopf algebras.

Abstract

To classify the finite dimensional pointed Hopf algebras with $G= {\rm McL}$ we obtain the representatives of conjugacy classes of $G$ and all character tables of centralizers of these representatives by means of software {\rm GAP}.