Let $G$ be a finite group. Two elements $x$ and $y$ of $G$ are said to be rationally conjugate, written $x \sim_{r} y$, if and only if $\langle x\rangle$ and $\langle y\rangle$ are conjugate subgroups of $G$. Let $A$ be the set of all character values of $G$, and let $H$ be the Galois group of the field extension $\mathbb{Q}(A)/\mathbb{Q}$. Is it true that the orbits of $H$ on conjugacy classes of $G$ are the same as the equivalence classes of $\sim_{r}$? Is there any proof or reference for this result?