From [Isaacs et.al. 2005][1]

> 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 ? 


  [1]: http://www.uv.es/amoquin/35.pdf