Example
Example. The symmetric group S3 has the following multiplication table.
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• e s t u v w e e s t u v w s s e v w t u t t u e s w v u u t w v e s v v w s e u t w w v u t s e
This group has six elements, so ord(S3) = 6. By definition, the order of the identity, e, is 1. Each of s, t, and w squares to e, so these group elements have order 2. Completing the enumeration, both u and v have order 3, for u2 = v and u3 = vu = e, and v2 = u and v3 = uv = e.
Read more about this topic: Order (group Theory)
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