Examples of finite groups with “good” bijection(s) between conjugacy classes and irreducible representations?
For symmetric group conjugacy classes and irreducible representation both are parametrized by Young diagramms, so there is a kind of "good" bijection between the two sets. For general finite groups ...
Is there an infinite group with exactly two conjugacy classes?
Berkovich mentioned the following result of Mann in his book on p-groups: The number of nonlinear irreducible characters of given degree in a p-group is divided by p-1. Do you know any reference for ...
Consider a finite group G. The product of conjugacy classes can be defined in natural way just by multiplying the representatives and counting multiplicities (see e.g. MO 62088). So we get ring with ...
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 ...