A characterization of the simple Ree groups \(^2 F_4( q^2)\) by their character codegrees (Q6146262)

Let \(G\) be a finite group and let \(\mathrm{Irr}(G)\) be the set of all irreducible complex characters of \(G\). If \(\chi \in \mathrm{Irr}(G)\), then the codegree of \(\chi\) (as defined in [\textit{G. Qian} et al., J. Algebra 312, No. 2, 946--955 (2007; Zbl 1127.20009)]) is the number \(\mathrm{cod}(\chi)=|G: \mathrm{ker}(\chi)| \cdot \chi(1)^{-1}\). In the paper under review, the author proves that the set of codegrees of the Ree groups \(^{2}F_{4}(q^{2})\) (where \(q^{2}=2^{2n+1}\)) determines such groups up to isomorphism.