From Isaacs et.al. 2005

Conjecture C. Let χ be a primitive irreducible character of an arbitrary finite group G. Then χ(1) divides | clG(g)| for some element g ∈ G.

Here, of course, we have written clG(g) to denote the class of g in G. We have checked that Conjecture C holds for all irreducible characters (primitive or not) of all groups in the Atlas 1.

Question 1 What is motivation for this ? Is it possible to describe what are conjugacy class(es) should correspond to irreducible representation in this way ?

Question 2 Is it still open ?