Categorisation of point groups by symmetry operations
This table lists point group symmetries along with their symmetry operations, the order of the group (i.e. the number of symmetry operations) and common notations. links to a correlation table, and links to tables of products of irreducible representations. The group produced by combination with inversion is listed under "x i". This, in the case of crystolographic point groups, is the Laue class which corresponds to the symmetry of reciprocal space. Isomorphic groups are also listed where character tables are available.
|E, C2, C2', C2''||4||D2 (V)||222||222||D2h||C2v, C2h|
|E, C2, v, v'||4||C2v||mm2||mm2||D2h||D2, C2h|
|E, C2, C2', C2'', i, , ', ''||8||D2h (Vh)||mmm||D2h|
Rhombic symmetry for defects in crystals is often divided into two
Type I: C2 coincides with the  direction and C2' and C2'' with  and [1-10] directions respectively (or, v and v' coincide with the planes (1-10) and (001)). Also belonging to type I are centres for which C2 coincides with  and v and v' with (110) and (1-10).
Type II: C2 axis coincides with  and the axes C2' and C2'' with  and , (or, alternatively, v and v' coincide with (010) and (100)).