# Periodicity

The following tables indicate the number of symmetry operations of a given period for each point group. If two point groups possess the same elements in the following tables, then they are termed isomorphic. Sets of isomorphic groups are form an abstract group (for example, C2h, C2v and D2).

The period of a symmetry operation is defined as the number of times that operation must be performed to be equivalent to the identity.

 Symmetry Operation: E Cn Sn i Period: 1 n n 2 2

 Period Period Pointgroup 1 2 3 4 5 6 Pointgroup 1 2 3 4 5 6 C1 1 C1h 1 1 C2 1 1 C2h 1 3 C3 1 1 C3h 1 1 4 C4 1 1 2 C4h 1 3 4 C5 1 4 C5h 1 1 8 C6 1 1 2 2 C6h 1 3 4 4 Period Period Pointgroup 1 2 3 4 5 6 Pointgroup 1 2 3 4 5 6 S2 1 1 C2v 1 3 C3v 1 3 2 S4 1 1 2 C4v 1 5 2 C5v 1 5 2 S6 1 1 2 2 C6v 1 7 2 2 Period Period Pointgroup 1 2 3 4 5 6 Pointgroup 1 2 3 4 5 6 D2 1 3 D2h 1 7 D3 1 2 3 D3h 1 7 4 D4 1 5 2 D4h 1 11 4 D5 1 5 4 D5h 1 11 8 D6 1 7 2 2 D6h 1 15 4 4

 Period Period Pointgroup 1 2 3 4 5 6 Pointgroup 1 2 3 4 5 6 8 10 12 T 1 3 8 D2d 1 5 2 Th 1 7 4 4 D3d 1 7 2 2 O 1 9 8 6 D4d 1 9 2 4 Td 1 9 8 6 D5d 1 11 4 4 Oh 1 19 8 12 8 D6d 1 11 2 2 2 4