International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by M. I. Aroyo

International Tables for Crystallography (2016). Vol. A, ch. 3.2, p. 721

Table 3.2.1.2 

Th. Hahna and H. Klappera

Table 3.2.1.2| top | pdf |
The 32 three-dimensional crystallographic point groups, arranged according to crystal system (cf. Chapter 2.1[link] )

Full Hermann–Mauguin (left) and Schoenflies symbols (right). The dashed line separates point groups with different Laue classes within one crystal system. A brief introduction to point-group symbols is provided in Hahn & Klapper (2005[link]).

General symbolCrystal system
TriclinicMonoclinic (top)
Orthorhombic (bottom)
TetragonalTrigonalHexagonalCubic
n 1 [C_{1}] 2 [C_{2}] 4 [C_{4}] 3 [C_{3}] 6 [C_{6}] 23 T
[\overline{n}] [\overline{1}] [C_{i}] [m \equiv \overline{2}] [C_{s}] [\overline{4}] [S_{4}] [\overline{3}] [C_{3{i}}] [\overline{6} \equiv 3/m] [C_{3h}]
[n/m]     [2/m] [C_{2h}] [4/m] [C_{4h}] [6/m] [C_{6h}] [2/m\overline{3}] [T_{h}]
n22     222 [D_{2}] 422 [D_{4}] 32 [D_{3}] 622 [D_{6}] 432 O
nmm     mm2 [C_{2v}] 4mm [C_{4v}] 3m [C_{3v}] 6mm [C_{6v}]
[\overline{n}2m]     [\overline{4}2m] [D_{2d}] [\overline{3}2/m] [D_{3d}] [\overline{6}2m] [D_{3h}] [\overline{4}3m] [T_{d}]
[n/m\, 2/m\, 2/m]     [2/m\, 2/m\, 2/m] [D_{2h}] [4/m\, 2/m\, 2/m] [D_{4h}] [6/m\, 2/m\, 2/m] [D_{6h}] [4/m\, \overline{3}\, 2/m] [O_{h}]