The character table of a sharply 5-transitive subgroup of ${\rm Alt}(12)$

TL;DR

This paper computes the character tables of specific sharply transitive subgroups of alternating groups without referencing Mathieu groups, using only their permutation representations.

Contribution

It provides a novel calculation method for character tables of sharply transitive groups relying solely on permutation representations, avoiding Mathieu group references.

Findings

Character table of sharply 5-transitive subgroup of Alt(12) computed

Character table of sharply 4-transitive subgroup of Alt(11) computed

New approach avoids Mathieu group references

Abstract

In this paper we calculate the character table of a sharply $5$-transitive subgroup of ${\rm Alt}(12)$, and of a sharply $4$-transitive subgroup of ${\rm Alt}(11)$. Our presentation of these calculations is new because we make no reference to the sporadic simple Mathieu groups, and instead deduce the desired character tables using only the existence of the stated multiply transitive permutation representations.