Let [Formula: see text] be a finite group and the codegree of an irreducible character [Formula: see text] is the number [Formula: see text]. In this paper, we consider nonsolvable groups with few character codegrees and prove that if a nonsolvable group [Formula: see text] has exactly four character codegrees, then [Formula: see text], where [Formula: see text].

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We obtain an improvement on the Casolo and Dolfi's result about ρ – σ conjecture for irreducible character degrees.