So i get the order of an element, but what about the order of a whole group. Keeping in using the order of 6, Using S_3 from (

Order (group theory) - Wikipedia, the free encyclopedia ) why is the order of the group S_3 equal 6? Now it says :

"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."

I don't see an element in S3 that has order 6...

Is the order of a group just mean the number of elements in the group?