Self-inverse conjugacy class

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Definition

Let $G$ be a group. A conjugacy class of $G$ is called a self-inverse conjugacy class if each element in the group is conjugate to its inverse, that is, each element of the conjugacy class is a real element. For this reason, the terminology real conjugacy class is sometimes also used, but this terminology can be ambiguous - see the page real conjugacy class for details.

Facts

In linear representation theory

• Number of real conjugacy classes is equal to number of irreducible real characters