FINITE GROUPS WITH FIVE NON-CENTRAL CONJUGACY CLASSES

Abstract. Let G be a nite group and Z(G) be the center of G. For a subset A of G, we dene kG(A), the number of conjugacy classes of G that intersect A non-trivially. In this paper, we ver- ify the structure of all nite groups G which satisfy the property kG(G ?? Z(G)) = 5; and classify them.