For a conjugacy class of a finite group, is central in its group algebra. In a complex irreducible representation of degree and character of a representation , it acts by ; its trace gives this formula and Schur lemma gives scalarity.
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In group theory, a branch of abstract algebra, the concept of a conjugacy class and the associated conjugacy class sum are important for understanding the structure of a group. ### Conjugacy Class A **conjugacy class** of an element \( g \) in a group \( G \) is the set of elements that can be obtained by conjugating \( g \) by all elements of \( G \).