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Let G be a finite group. Denote by Irr(G) the set of all irreducible complex characters of G. Let $${{\rm cd}(G)=\{\chi(1)\;|\;\chi\in {\rm Irr}(G)\}}$$ be the set of all irreducible complex character degrees of G forgetting multiplicities, and let X1(G) be the set of all irreducible complex character degrees of G counting multiplicities. Let H be any non-abelian simple exceptional group of Lie type. In this paper, we will show that if S is a non-abelian simple group and $${{\rm cd}(S)\subseteq {\rm cd}(H)}$$ then S must be isomorphic to H. As a consequence, we show that if G is a finite group with $${{\rm X}_1(G)\subseteq {\rm X}_1(H)}$$ then G is isomorphic to H. In particular, this implies that the simple exceptional groups of Lie type are uniquely determined by the structure of their complex group algebras.

Simple exceptional groups of Lie type are determined by their character degrees