Itô's Theorem

The dimension $d$ of any Irreducible Representation of a Group $G$ must be a Divisor of the index of each maximal normal Abelian Subgroup of $G$.

See also Abelian Group, Irreducible Representation, Subgroup

References

Lomont, J. S. Applications of Finite Groups. New York: Dover, p. 55, 1993.