
Cubic 
(T T_{h} O T_{d} O_{h}) 
Tetragonal 
(C_{4} S_{4} C_{4h} D_{4} C_{4v} D_{2d} D_{4h}) 
Orthorhombic 
Operations 
Order 
Schönflies Symbol 
International Symbol 
Full Symmetry Symbol 
Correlation Table 
Irred. Rep. products 
× i 
Isomorph. with 
E, C_{2}, C_{2}’, C_{2}’’ 
4 
D_{2}(V) 
222 
222 

⊗ 
D_{2h} 
C_{2v}, C_{2h} 
E, C_{2}, σ_{v}, σ_{v}’ 
4 
C_{2v} 
mm2 
mm2 

⊗ 
D_{2h} 
D_{2}, C_{2h} 
E, C_{2}, C_{2}’, C_{2}’’, i, σ, σ’, σ’’ 
8 
D_{2h}(V_{h}) 
mmm 


⊗ 
D_{2h} 

Rhombic symmetry for defects in cubic crystals is often pided into two types: Type I: C_{2} coincides with the [110] direction and C_{2}’ and C_{2}’’ with [001] and [110] directions respectively (or, σ_{v} and σ_{v}’ coincide with the planes (110) and (001)). Also belonging to type I are centres for which C_{2} coincides with [001] and σ_{v} and σ_{v}’ with (110) and (110). Type II: C_{2} axis coincides with [001] and the axes C_{2}’ and C_{2}’’ with [100] and [010], (or, alternatively, σ_{v} and σ_{v}’ coincide with (010) and (100)). 
Monoclinic 
(C_{2} C_{s} C_{2h}) 
Triclinic 
(C_{1} C_{i}) 
Trigonal 
(C_{3} S_{6} D_{3} C_{3v} D_{3d}) 
Hexagonal 
(C_{6} C_{3h} C_{6h} D_{6} C_{6v} D_{3h} D_{6h}) 
Noncrystallographic 
(C_{∞} C_{∞h} C_{∞v} D_{∞h} C_{5} S_{8} D_{5} C_{5v} C_{5h} D_{4d} D_{5d} D_{5h} D_{6d} I_{} I_{h}) 
All 
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 "× 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. 