 Automorphisms of the symmetric group

An automorphism preserving the transposition class is inner: commuting relations recover the vertex stars of the complete graph, with a small-case adjustment in degrees three and four. An involution class has the same size as the transposition class only in degree six, when triple transpositions also have size fifteen. Hence outer automorphism groups of symmetric groups are trivial outside degree six and have size at most two in degree six.

// Target: combinatorics.bigb