Divisions of a group (reviewed)

A division (or rational conjugacy classes) of a finite group $G$ is an equivalence class under the following relation: $x \sim y$ if there exist $g \in G$ and $n \in \Z$ relatively prime to the order of $x$ with $y = g^{-1} x^n g$. It is a coarsening of conjugacy: any division is a union of conjugacy classes.

Just as values of characters are constant on conjugacy classes, values of rational characters are constant on rational conjugacy classes.