# Definition A [[group]] is *Abelian* (or *commutative*) if it satisfies *Commutativity*: $x\bullet y = y \bullet x \, \forall x, y \in G$ All elements of an Abelian group are [[Conjugacy Class|self-conjugate]], and thus they belond to their own [[conjugacy class]]. This means that the number of [[Irreducible Representation|irreducible representations]] of an Abelian group is equal to its [[Group Order|order]].