In abstract algebra, the symmetric group S_n on a finite set of n symbols is the group whose elements are all the permutation operations that can be performed on n distinct symbols, and whose group operation is the composition of such permutation operations, which are defined as bijective functions from the set of symbols to itself. Since there are n! (n factorial) possible permutation operations that can be performed on a tuple composed of n symbols, it follows that the order (the number of elements) of the symmetric group S_n is n!.