Symmetric Group (All Permutations)

The symmetric group $S_n$, also sometimes just called the permutation group, consists of all permutations of $n$ objects. These objects being permuted can be labeled cards, or points, or whatever else you want. In isomorphic ciphers, the $n$ letters of the ciphertext alphabet are the objects being permuted.

The alternating group $A_n$ consists of all even permutations, and I'm not going to make a separate page for it... Or should I? Hm