Nonsolvable Groups with Three Nonlinear Irreducible Character Codegrees∗

For an irreducible character χ of a finite group G, the codegree of χ is defined as |G : ker(χ)|/χ(1). In this paper, the authors determine finite nonsolvable groups with exactly three nonlinear irreducible character codegrees, which are L2(2f ) for f ≥ 2, PGL2(q) for odd q ≥ 5 or M10.