The order of the representative elements of conjugacy classes

Question

Suppose $A$ is an arbitrary subset of group $G$ and $K_G(A)$ be the number of $G$-conjugacy classes contained in $A$. A finite group $G$ satisfies property $P_n$ if for every prime integer $p$, $G$ has at most $n-1$ noncentral conjugacy classes the order of the representative element of which is a multiple of $p$. Now if $G$ be a nonsolvable group satisfying property $P_5$, $N= G^{'}Z(G)$, $G/N$ be abelian and $|G/N|=2, 3, 4, 5$ or 6. What can we say about $K_G(G-N)$?