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

International Tables for Crystallography (2006). Vol. D, ch. 1.2, pp. 58-60

## Table 1.2.6.5

T. Janssena*

aInstitute for Theoretical Physics, University of Nijmegen, 6524 ED Nijmegen, The Netherlands
Correspondence e-mail: ted@sci.kun.nl

 Table 1.2.6.5| top | pdf | Irreducible representations and character tables for the 32 crystallographic point groups in three dimensions
 (a)
 n 1 Order 1 1
 (b)
 n 1 1 Order 1 2 1 1 1 −1
 z z
 (c) [].
 n 1 1 1 Order 1 3 3 1 1 1 1 1
 Matrices of the real two-dimensional representation:

 z
 (d)
n1
Order1
1
1
1
1
 Matrices of the real two-dimensional representation:

 z z
 (e) [].
n1
Order1
1
1
1
1
1
1
 Matrices of the real representations:

 z : : z : : z : :
 (f)
n1
Order1
1
1
1
1
 x y z z y x z z
 (g)
n
Order
 Matrices of the two-dimensional representation:

 z z
 (h)
n1
Order1
1
1
1
1
2
 Matrices of the two-dimensional representation:

 422 z z z
 (i)
n1
Order1
1
1
1
1
2
2
 Matrices of the two-dimensional representations:

 z z z z
 (j) T [].
T
n144
Order133
1 1 1
1
1
3 0 0
 Real representations of dimension :

 T
 (k) O
O
n1
Order1
1
1
2
3
3
 Higher-dimensional representations:

 O
 Other point groups which are of second class and contain . See Table 1.2.6.6(a).
GroupIsomorphism classRotation subgroup
4
6
222
422
622
23
432