Huppert's Conjecture for $Fi_{23}$

Abstract

Let $G$ denote a finite group and $\text{cd}(G)$ the set of irreducible character degrees of $G$. Bertram Huppert conjectured that if $H$ is a finite nonabelian simple group such that $\text{cd}(G) =\text{cd}(H)$, then $G\cong H \times A$, where $A$ is an abelian group. Huppert verified the conjecture for many of the sporadic simple groups. We illustrate the arguments by presenting the verification of Huppert's Conjecture for $Fi\_{23}$.