Let $G$ be a finite group and $\mathrm{ Irr}(G)$ the set of all irreducible complex characters of $G$. Define the codegree of $\chi \in \mathrm{ Irr}(G)$ as $\mathrm{ cod}(\chi):=\frac{ |G:\mathrm{ ker}(\chi) |}{ \chi(1)}$ and denote by $\mathrm{ cod}(G):=\{ \mathrm{ cod}(\chi)|\chi\in \mathrm{ Irr}(G)\}$ the codegree set of $G$. Let $H$ be one of the $26$ sporadic simple groups. In this paper, we show that $H$ is determined up to isomorphism by cod$(H)$.
Categories: math.GR