On the characterization of some non-abelian simple groups using codegree set

Let $G$ be a finite group and $\chi \in \text{irr}(G)$. The codegree of $\chi$ is defined as $\text{cod}(\chi )=\frac{\mathrm{\mid }G:\ker (\chi )\mathrm{\mid }}{\chi (1)}$ and $\text{cod}(G)=\{\text{cod}(\chi )\mathrm{\mid }\chi \in \text{irr}(G)\}$ is called the set of codegrees of $G$. In this paper, we show that the set of codegrees of ${\text{Sy}}_4(4),{\text{U}}_4(2)$, ${\text{Sy}}_4(q)(q\ge 4)$, ${\text{U}}_4(3)$, ${}^2{\text{F}}_4(2{)}^{\mathrm{\prime }}$, ${\text{J}}_3$, ${\text{G}}_2(3)$, ${\text{A}}_9$, ${\text{J}}_2$, $\text{PSL}(4,3)$, $\text{McL}$, ${\text{Sy}}_4(5)$, ${\text{G}}_2(4)$, $\text{HS}$, $\text{ON}$ and ${\text{M}}_{24}$ determines the group up to isomorphism.