A group is called finite if it has a finite number of elements. The number of elements is called the order of the group. An important class is the symmetric groups ⁠ S N ⁠, the groups of permutations of N objects. For example, the symmetric group on 3 letters S 3 is the group of all possible reorderings of the objects. The three letters ABC can be reordered into ABC, ACB, BAC, BCA, CAB, CBA, forming in total 6 (factorial of 3) elements. The group operation is composition of these reorderings, and the identity element is the reordering operation that leaves the order unchanged. This class is fundamental insofar as any finite group can be expressed as a subgroup of a symmetric group S N for a suitable integer ⁠ N ⁠, according to Cayley's theorem. Parallel to the group of symmetries of the square above, S 3 can also be interpreted as the group of symmetries of an equilateral triangle.