The set of all centralizers elements in a finite group G is denoted by Cent(G) and called n-centralizer if |Cent(G)|=n. In this paper, the structure non-abelian with property that GZ(G)≅Zp2⋊Zp2 obtained. As consequence, it proved such has exactly [(p+1)2+1] element commuting conjugacy class graph completely determined.