Minimal faithful permutation degrees for irreducible Coxeter groups and binary polyhedral groups

The minimal faithful permutation degree of a finite group G, denoted by \mu(G), is the least non-negative integer n such that G embeds inside Sym(n). 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.