In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions. In particular, the finite symmetric group formula_1 defined over a finite set of formula_2 symbols consists of the permutations that can be performed on the formula_2 symbols. Since there are formula_4 (formula_2 factorial) such permutation operations, the order (number of elements) of the symmetric group formula_1 is formula_4.