Let $G$ be a finite group and let $g \in G$ be an element of order $pq$, where $p < q$ are 
prime numbers. Denote by $g^G$ the conjugacy class of $g$ in $G$. Under which conditions
does the following hold?:
$$
 |(g^p)^G| = |(g^q)^G| = |(g^{q−p})^G|
$$
-- Is it possible that this happens?