The character tables of centralizers in Sporadic Simple Groups of ${\rm HS}$ and ${\rm Co_3}$

TL;DR

This paper computes the character tables of centralizers in the sporadic simple groups HS and Co3 using GAP, aiding the classification of related finite-dimensional pointed Hopf algebras.

Contribution

It provides the first complete character tables of centralizers in HS and Co3, essential for algebraic classification tasks.

Findings

Character tables of all centralizers in HS and Co3 are obtained.

Conjugacy class representatives are identified.

Results facilitate classification of pointed Hopf algebras.

Abstract

To classify the finite dimensional pointed Hopf algebras with $G= {\rm HS}$ or ${\rm Co3}$ we obtain the representatives of conjugacy classes of $G$ and all character tables of centralizers of these representatives by means of software {\rm GAP}.