Huppert's Conjecture for $Fi_{23}$

Let G denote a finite group and cd(G) the set of irreducible character degrees of G. Bertram Huppert conjectured that if H is a finite nonabelian simple group such that cd(G) = cd(H), then G ∼= H × 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 Fi23.