Corollary $11.29$ of the book Character Theory of Finite Groups by I. Martin Isaacs as given:
Corollary $11.29:$ Let $H$ be a normal subgroup of $G$ and $\zeta\in Irr(G), \xi\in Irr(H)$, be a constituent of $\zeta_{H}$. Then $\zeta(1)/ \xi(1)$ divides $|G:H|.$
My question is can i say that above corollary is valid over any field or only for $C?$ Please suggest. Thanks.