If $G$ is a finite group, then it is well known that there are finitely many inequivalent irreducible representations of $G$ over $\mathbb{C}$; moreover the sum of squares of dimensions of the representations is equal to $|G|$. Also, the dimension of representation divides $|G|$.
If we consider representations over $\mathbb{Q}$, are the dimensions of irreducible representations related to $|G|$ in such a nice way?