Frobenius group and conjugacy relation

Question

I try to solve the following problem (problem 6.A.4 from M.Isaacs Ginite Group Theory)

Let $G$ be a Frobenius group with Frobenius kernel $N$. Show that each coset of $N$ in $G$ other than $N$ itself is contained in a single conjugacy class of $G$.

My attempt was to show that $Ng \subseteq g^G$ for every $g\notin N$, but I cannot prove this. Also I tried to prove by the contrary but also stuck.

Answer 1

$C_N(g)=1$ so $g$ has $|N|$ conjugates under $N$, which. must be the elements of $Ng$.