Minimal Faithful Permutation Degrees for Irreducible Coxeter Groups and Binary Polyhedral Groups

TL;DR

This paper determines the smallest degree of faithful permutation representations for all irreducible Coxeter groups and presents new examples of finite groups with quotients having higher minimal degrees.

Contribution

It provides explicit calculations of minimal faithful permutation degrees for irreducible Coxeter groups and introduces novel examples of finite groups with larger quotient degrees.

Findings

Minimal faithful permutation degrees for all irreducible Coxeter groups are computed.

New examples of finite groups with quotients of higher minimal degree are constructed.

The relationship between group quotients and permutation degrees is explored.

Abstract

In this article we calculate the minimal faithful permutation degree for all of the irreducible Coxeter groups. We also exhibit new examples of finite groups that possess a quotient whose minimal degree is strictly greater than that of the group.