Tables for
Volume D
Physical properties of crystals
Edited by A. Authier

International Tables for Crystallography (2006). Vol. D, ch. 1.2, p. 57


T. Janssena*

aInstitute for Theoretical Physics, University of Nijmegen, 6524 ED Nijmegen, The Netherlands
Correspondence e-mail:

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Finite point groups in three dimensions

Isomorphism classFirst class with determinants [\gt\,0]Second class with −EThird class without −EOrder
[ C_{n}] n   [\bar{n}] (n even, [\,\gt\,]2) [n]
      m ([n=2])  
[D_{n}] n22 (n even)   [nmm] (n even) [2n]
  n2 (n odd, [\gt\,1])   [\bar{n}2m] (n even)  
      [nm] (n odd)  
[C_{n}\times C_{2}]   [\bar{n}] (n odd)   [2n]
    [n/m] (n even)    
[D_{n}\times C_{2}]   [n/mmm] (n even, [\geq 4])   [4n]
    [mmm] ([n=2])    
    [\bar{n}m] (n odd, [\gt\,0])    
T 23     [12]
O 432   [\bar{4}3m] [24]
I 532     [60]
[T\times C_{2}]   [m\bar{3}]   [24]
[O\times C_{2}]   [m\bar{3}m]   [48]
[I\times C_{2}]   [\bar{5}\bar{3}m]   [120]