On the characterization of some non-abelian simple groups using codegree set

Abstract

Let G be a finite group and χ ∈ Irr ( G ) . The codegree of χ is defined as cod ( χ ) = | G : ker ( χ ) | / χ ( 1 ) and cod ( G ) = { cod ( χ ) | χ ∈ Irr ( G ) } is called the set of codegrees of G. In this paper, we show that the set of codegrees of U 4 ( 2 ) , S 4 ( q ) ( q = 2 f ≥ 4 ) , U 4 ( 3 ) , 2 F 4 ( 2 ) ′ , J 3 , G 2 ( 3 ) , A 9 , J 2 , PSL ( 4 , 3 ) , McL , S 4 ( 5 ) , G 2 ( 4 ) , HS , O ′ N and M 24 determines the group up to isomorphism.