Laue groups are the 11 characteristic centrosymmetric point groups (in yellow) as listed in Table 1677a. The Laue groups are obtained by adding a center of symmetry to each point group.
Table 1677a. Centrosymmetric, noncentrosymmetric, and chiral space groups.
Crystal system 
Laue group 
Point group 
Space group 
International notation 
Schoenflies notation 
Triclinic 
1 
1 
C_{1} 
P1 
1 
C_{i} 
P1 
Monoclinic 
2/m 
2 
C_{2} 
P2, P2_{1}, C2 
m 
C_{1h} 
Pm, Pc, Cm, Cc 
2/m 
C_{2h} 
P2/m, P2_{1}/m, C2/m, P2/c, P2_{1}/c, C2/c 
Orthorhombic 
mmm 
222 
D_{2} 
P222, P222_{1}, P2_{1}2_{1}2, P2_{1}2_{1}2_{1}, C222, C222_{1}, I222, I2_{1}2_{1}2_{1}, F222 
mm2 
C_{2v} 
Pmm2, Pmc2_{1}, Pcc2, Pma2, Pca2_{1}, Pnc2, Pmn2_{1}, Pba2, Pna2_{1}, Pnn2, Cmm2, Cmc2_{1}, Ccc2, Amm2, Abm2, Ama2, Aba2, Imm2, Iba2, Ima2, Fmm2, Fdd2 
mmm 
D_{2h} 
Pmmm, Pnnn, Pccm, Pban, Pmma, Pnna, Pmna, Pcca, Pbam, Pccn, Pbcm, Pnnm, Pmmn, Pbcn, Pbca, Pnma, Cmcm, Cmca, Cmmm, Cccm, Cmma, Ccca, Immm, Ibam, Ibca, Imma, Fmmm, Fddd 
Tetragonal 

4 
C_{4} 
P4, P4_{1}, P4_{2}, P4_{3}, I4, I4_{1} 

422 
D_{4} 
P422, P42_{1}2, P4_{1}22, P4_{1}2_{1}2, P4_{2}22, P4_{2}2_{1}2, P4_{3}22, P4_{3}2_{1}2, I422, I4_{1}22 

4 
S_{4} 


4mm 
C_{4v} 


42m 
D_{2d} 


4/m 
C_{4h} 


4/mmm 
D_{4h} 

Trigonal 

3 
C_{3} 


32 
D_{3} 


3m 
C_{3v} 


3 
S_{6} 


3m 
D_{3d} 

Hexagonal 

6 
C_{6} 


622 
D_{6} 


6 
C_{3h} 


6mm 
C_{6v} 


6m2 
D_{3h} 


6/m 
C_{6h} 


6/mmm 
D_{6h} 

Cubic 

23 
T 


432 
O 


43m 
T_{d} 


m3 
T_{h} 


m3m 
O_{h} 

Red: chiral; green: noncentrosymmetric; and yellow: centrosymmetric. 
Table 1677b. Other characteristics of noncentrosymmetric space groups.
Difference between centrosymmetric, noncentrosymmetric, and chiral space groups 
page1675 
Two centrosymmetric reciprocal lattice points (hkl) and (hkl) are called Friedel (or Bijvoet) pair. Friedel's law describes the relationship between the structure amplitude of the two centrosymmetric reciprocal lattice points. According to the Friedel's law, regardless of whether the crystal structure is centrosymmetric or not, if there is no anomalous scattering the reciprocal space is always centrosymmetric, given by,
F(hkl) = F(hkl)  [1677]
The square of F represents the intensity of the peak of the corresponding reciprocal lattice point. Therefore, it is difficult to distinguish if the space group of a material is centrosymmetric or noncentrosymmetric.
However, there are still different ways to distinguish if the crystal belongs to centrosymmetric or noncentrosymmetric space groups:
i) Distinguished by its symmetry elements. For instance, if there is x,y,z in its symmetry elements, the crystal is centrosymmetric (i.e. contains the center of
inversion); otherwise, noncentrosymmetric. For instance, Pca2_{1} (see page1850) and Pbca (see page3016) space groups are noncentrosymmetric and centrosymmetric, respectively.
ii) Distringuished by the physical properties. For instance, a ferroelectric material must belong to a noncentrosymmetric space group.
iii) Distringuished by CBED, which can be sensitive enough to detect the polarization of crystals.
iv) Distringusihed by the intensity statistics of Xray diffraction.
