 Automorphisms of the symmetric and alternating groups

In group theory, a branch of mathematics, the automorphisms and outer automorphisms of the symmetric groups and alternating groups are both standard examples of these automorphisms, and objects of study in their own right, particularly the exceptional outer automorphism of S6, the symmetric group on 6 elements.Among symmetric groups, only S6 has a non-trivial outer automorphism,
which one can call "exceptional" (in analogy with exceptional Lie algebras) or "exotic".