Let G be a finite group and $#$Cent(G) denote the number of centralizers of its elements. G is called n-centralizer if $#$Cent(G) = n, and primitive n-centralizer if $#$Cent(G) = $#$Cent($frac{G}{Z(G)}$) = n. In this paper we investigate the structure of finite groups with at most 21 element centralizers. We prove that such a group is solvable and if G is a finite group such that G/Z(G)$simeq$$A_5$, then $#$Cent(G) = 22 or 32. Moreover, we prove that As is the only finite simple group with 22 centralizers. Therefore we obtain a characterization of As in terms of the number of centralizers