A conjugacy class is a particular subset of a group.
Let be a group. Consider the action of on itself by inner automorphisms. The orbits of are then called conjugacy classes. By expanding the definition, it is easy to show that two elements and are in the same conjugacy class iff there is an element such that .
Two subsets and of are called conjugate if there exists for which is the image of under .
The character of any group are constant on conjugacy classes.
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