M. Rezaei - Department of Mathematics, Buein Zahra Technical University, Buein Zahra, Qazvin, Iran.
Z. Foruzanfar - Buein Zahra Technical University, Buein Zahra, Qazvin, Iran.

‎Let G be a finite group and Z(G) be the center of G‎. ‎For a subset A of G‎, ‎we define kG(A)‎, ‎the number of conjugacy classes of G that intersect A non-trivially‎. ‎In this paper‎, ‎we verify the structure of all finite groups G which satisfy the property kG(G-Z(G))=5, and classify them‎.

‎Finite group‎, ‎Frobenius group‎, ‎Conjugacy class