= 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
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