1.NounA subset of a group which is an equivalence class in the quotient set of the group divided by conjugation as equivalence relation.
"For a given element
x
{\displaystyle x}
of some group
G
{\displaystyle G}
, its conjugacy class
x
G
{\displaystyle x^{G}}
is
{
y
∈
G
|
∃
g
∈
G
:
g
−
1
x
g
=
y
}
{\displaystyle \{y\in G|\exists g\in G:g^{-1}xg=y\}}
.; If a group acts on itself through conjugation, then its orbits are its conjugacy classes and its stabilizer subgroups are its centralizers."