In this talk, we shall show that for each positive integer n, there are only finitely many groups G, up to isoclinism, with w(G) = n, and we obtain similar results for groups with exactly n centralizers. Where a subset X of a group G is a set of pairwise noncommuting elements if ab 6= ba for any two distinct elements a and b 2 X. If jXj jY j for any other set of pairwise noncommuting elements Y in G, then X is called a maximal subset of pairwise noncommuting elements and the cardinality of such a subset (if it exists) is denoted by !(G).
