# Character-conjugate conjugacy classes

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This term is related to: linear representation theory

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## Definition

Two conjugacy classes in a group are said to be **character-conjugate** if for every finite-dimensional indecomposable linear representation (and hence any finite-dimensional linear representation) of the group, the value that the character of the representation takes on both the conjugacy classes is equal.

## Relation with other properties

### Stronger properties

## Facts

It turns out that for a finite group, and a field whose characteristic does not divide the order of the group, character-conjugate conjugacy classes are the same as locally conjugate conjugacy classes.