Abstract
Let G be a finite group of odd order. We show that if χ is an irreducible primitive character of G then for all primes p dividing the order of G there is a conjugacy class such that the p-part of χ(1) divides the size of that conjugacy class. We also show that for some classes of groups the entire degree of an irreducible primitive character χ divides the size of a conjugacy class.
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