Editing Order (group theory) (section)

==Class equation<!--linked from 'Vertical bar'-->==
An important result about orders is the [[class equation]]; it relates the order of a finite group ''G'' to the order of its [[center of a group|center]] Z(''G'') and the sizes of its non-trivial [[conjugacy class]]es:
:<math>|G| = |Z(G)| + \sum_{i}d_i\;</math>
where the ''d<sub>i</sub>'' are the sizes of the non-trivial conjugacy classes; these are proper divisors of |''G''| bigger than one, and they are also equal to the indices of the centralizers  in ''G'' of the representatives of the non-trivial conjugacy classes. For example, the center of S<sub>3</sub> is just the trivial group with the single element ''e'', and the equation reads |S<sub>3</sub>|&nbsp;= 1+2+3.