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Semi direct product group

If G=MV, 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 conjugacyclass. I would like to prove |f^-1(m)\cap C_x|>=p, m\in M. Do you think such result is true? Best reagrds Ha.