Suppose $G=V \rtimes M$, is a semi product group of an elementary abelian p-group of size $|V|=p^e$ and $M$ is a subgroup of $G$. If $f$ is the natural projection from $G$ onto $M$. $C_x=\{x^G\}$ is a conjugacy class. I would like to prove $|f^{-1}(m)\cap C_x|\geq p, m\in M$. Do you think such result is true? Best regards Ha.