→For finite groups over a splitting field
===For finite groups over a splitting field===
A [[splitting field]] is a field of characteristic not dividing the order of the group whereby the irreducible representations over that field remain irreducible in all bigger fields.
We have the following:
* [[Number of irreducible representations equals number of conjugacy classes]]
In addition, there are a number of other combinatorial and arithmetic controls on the nature and degrees of irreducible representations. For more, see [[degrees of irreducible representations]].
==Relation with other properties==