# THE EXCEPTIONAL SYMMETRY

@article{McCammond2014THEES, title={THE EXCEPTIONAL SYMMETRY}, author={Jon McCammond}, journal={arXiv: Group Theory}, year={2014} }

This note gives an elementary proof that the symmetric groups possess only one exceptional symmetry. I am referring to the fact that the outer automorphism group of the symmetric group Symn is trivial unless n = 6 and the outer automorphism group of Sym6 has a unique nontrivial element. When we study symmetric groups, we often invoke their natural faithful representation as permutations of a set without a second thought, but to what extent is this representation intrinsic to the structure of… Expand

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