Nonsolvable groups with three nonlinear irreducible character codegrees
Dongfang Yang, Yu Zeng · arXiv (Cornell University) · 2022
For an irreducible character $χ$ of a finite group $G$, the codegree of $χ$ is defined as $|G:\ker(χ)|/χ(1)$. In this paper, we determine finite nonsolvable groups with exactly three nonlinear irreducible character codegrees, and they are $\mathrm{L}_2(2^f)$ for $f\ge 2$, $\mathrm{PGL}_2(q)$ for odd $q\ge 5$ or $\mathrm{M}_{10}$.