Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of permutations on a set of n-elements is denoted S_n. Symmetric groups capture the history of abstract algebra, provide a wide range of examples in group theory, are useful when writing software to study abstract algebra, and every finite group can be represented as a subgroup of a symmetric group. This result is known as Cayley's Theorem.