Let

*a* be an element of a

group *G*. The

conjugacy class
of

*a* consists of all

conjugates of

*a*
*Conj(a)={gag*^{-1} such that

*g* in

*G}*
The conjugacy classes of the elements of *G* are equivalence classes
for the equivalence relation on *G*
given by *aRb* iff there exists *x* in *G* such that
*b=xax*^{-1}. As such the conjugacy classes of *G*
partition *G*. See also centralizer.