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

International Tables for Crystallography (2006). Vol. D, ch. 1.2, p. 62

Table 1.2.6.9 

T. Janssena*

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

Table 1.2.6.9| top | pdf |
Number of free parameters of some tensors

GroupIsomorphism classCharacter of the vector representationMultiplicity identity representation in
[\Gamma^{\otimes 2}][\Gamma_{s}^{\otimes 2}][\Gamma^{\otimes 3}][\Gamma \otimes \Gamma_{s}^{\otimes 2}][\left(\Gamma_{s}^{\otimes 2} \right)_{s} ^{\otimes 2}]
1 [C_{1}] 3 9 6 27 18 21
[\bar{1}] [C_{2}] 3, −3 9 6 0 0 21
2 [C_{2}] 3, −1 5 4 13 8 13
m [C_{2}] 3, 1 5 4 14 10 13
[2/m] [C_{2}\times C_2]   5 4 0 0 13
222 [D_2] 3, −1, −1, −1 3 3 6 3 9
[2mm] [ D_2] 3, 1, 1, −1 3 3 7 5 9
[mmm] [D_{2}\times C_2]   3 3 0 0 9
3 [C_3] 3, 0, 0 3 2 9 6 9
[\bar{3}] [C_3\times C_2]   3 2 0 0 9
32 [D_3] 3, 0, −1 2 2 4 2 6
[3m] [D_3] 3, 0, 1 2 2 5 4 6
[\bar{3}m] [D_3\times C_2]   2 2 0 0 6
6 [C_6] 3, 2, 0, −1, 0, 2 3 2 7 4 5
[\bar{6}] [C_6] 3, 2, 0, 1, 0, −2 3 2 2 2 5
[6/m] [C_6\times C_2]   3 2 0 0 5
622 [D_6] 3, 2, 0, −1, −1, −1 2 2 3 1 5
[6mm] [D_6] 3, 2, 0, −1, 1, 1 2 2 4 3 5
[\bar {6}2m] [D_6] 3, −2, 0, 1, −1, 1 2 2 1 1 5
[6/mmm] [D_6\times C_2]   2 2 0 0 5
4 [C_4] 3, 1, −1, 1 3 2 7 4 7
[\bar{4}] [C_4] 3, −1, −1, −1 3 2 6 4 7
[4/m] [C_4\times C_2]   3 2 0 0 7
422 [D_4] 3, 1, −1, −1, −1 2 2 3 1 6
[4mm] [D_4] 3, 1, −1, 1, 1 2 2 4 3 6
[\bar {4}2m] [D_4] 3, −1, −1, −1, 1 2 2 3 2 6
[4/mmm] [D_4\times C_2]   2 2 0 0 6
23 T 3, 0, 0, −1 1 1 2 1 3
[m3] [T\times C_2]   1 1 0 0 3
432 O 3, 0, −1, 1, −1 1 1 1 0 3
[\bar{4}3m] O 3, 0, −1, −1, 1 1 1 1 1 3
[m3m] [O\times C_2]   1 1 0 0 3