
Operations 
Order 
Schönflies Symbol 
International Symbol 
Full Symmetry Symbol 
Correlation Table 
Irred. Rep. products 
× i 
Isomorph. with 
Piezoelectric Classes 
Pyroelectric Classes 
E 
1 
C_{1} 
1 
1 

⊗ 
C_{i} 
E, C_{2} 
2 
C_{2} 
2 
2 

⊗ 
C_{2h} 
C_{s}, C_{i} 
E, σ_{h} 
2 
C_{s}(C_{1h}) 
m 
m 

⊗ 
C_{2h} 
C_{2}, C_{i} 
E, C_{3}, C_{3}^{2} 
3 
C_{3} 
3 
3 

⊗ 
S_{6} 

E, C_{4}, C_{2}, C_{4}^{3} 
4 
C_{4} 
4 
4 

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

⊗ 
D_{2h} 
D_{2}, C_{2h} 
E, 2C_{3}, 3σ_{v} 
6 
C_{3v} 
3m 
3m 

⊗ 
D_{3d} 
D_{3} 
E, C_{6}, C_{3}, C_{2}, C_{3}^{2}, C_{6}^{5} 
6 
C_{6} 
6 
6 

⊗ 
C_{6h} 
S_{6}, C_{3h} 
E, 2C_{4}, C_{2}, 2σ_{v}, 2σ_{d} 
8 
C_{4v} 
4mm 
4mm 

⊗ 
D_{4h} 
D_{4}, D_{2d} 
E, 2C_{6}, 2C_{3}, C_{2}, 3σ_{v}, 3σ_{d} 
12 
C_{6v} 
6mm 
6mm 

⊗ 
D_{6h} 
D_{6}, D_{3d}, D_{3h} 
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. 