Conjugacy class
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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