Character degrees of extensions of the Suzuki groups $^2B_2(q^2)$

TL;DR

This paper determines the degrees of all complex irreducible characters for groups lying between a Suzuki group and its automorphism group, enriching the understanding of their representation theory.

Contribution

It explicitly computes the character degrees of all groups extending a Suzuki group, a novel contribution to the representation theory of these groups.

Findings

Character degrees of groups between $^2B_2(q^2)$ and its automorphism group are fully determined.

Provides explicit formulas for the degrees of irreducible characters.

Enhances understanding of the structure and representations of Suzuki groups.

Abstract

Let $S$ be a Suzuki group $^2B_2(q^2)$, where $q^2=2^{2f+1}$, $f\geqslant 1$. In this paper, we determine the degrees of the ordinary complex irreducible characters of every group $G$ such that $S\leqslant G\leqslant \Aut(S)$.