For a finite group G , let $v(G)$ denote the number of conjugacy (G)\\vert amp;#??;?$ if and only if $G\\cong A_{?}$.\\\\ We show that if $G$ is a finite group , then $v(G)=?$ if and only if $G\\cong Q\\rtimes P$ where $Q\\cong \\mathbb{Z}_q$ , $P\\cong \\mathbb{Z}_{p^n}$ and $[Q,\\Phi (P)]=?$ where $p$ and $q$ primes with $p|\\; q-?$; or $G\\cong M_{p^{n amp;#??;?}}$ , where $\\langle g,h\\; |\\; g^{p^n}=h^p =?,\\; g^h = g^{? amp;#??;p^{n-?}}\\rangle$ , \\ $n\\geq ?$ if $p gt; ?$ , and $n\\geq ?$ if $p=?$.\\\\ We also show that if $G$ is a finite nilpotent group such that $v(G)\\leq\\vert\\pi(G)\\vert$ .
