In odd-order finite groups, the p-part of the degree of any irreducible primitive character divides the size of some conjugacy class for each prime p dividing |G|.
Gajendragadkar, A characteristic class of characters of finite π-separable groups, Journal of algebra, 59 (1979), pp
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Primitive characters of odd order groups
In odd-order finite groups, the p-part of the degree of any irreducible primitive character divides the size of some conjugacy class for each prime p dividing |G|.