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. 60

Table 1.2.6.6 

T. Janssena*

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

Table 1.2.6.6| top | pdf |
Direct products with [\{E,\bar{1}\}] and [\{E,1'\}]

(a) With [\{E,\bar{1}\}].

[K\times {\bb Z}_{2}][R\in K][\bar{R}]
[ \Gamma_{g}] [\chi (R)] [\chi (R)]
[\Gamma_{u}] [\chi (R)] [-\chi (R)]

[4/m] [C_{4}\times {\bb Z}_{2}] cf. 4
[6/m] [C_{6}\times {\bb Z}_{2}] cf. 6
[mmm] [D_{2}\times {\bb Z}_{2}] cf. 222
[4/mmm] [D_{4}\times{\bb Z}_{2}] cf. 422
[6/mmm] [D_{6}\times{\bb Z}_{2}] cf. 622
[m\bar{3}] [T\times{\bb Z}_{2}] cf. 23
[m\bar{3}m] [O\times{\bb Z}_{2}] cf. 432

(b) With [\{E,1'\}].

[K\times {\bb Z}_{2}][R\in K][R']
[ \Gamma_{+}] [\chi (R)] [\chi (R)]
[\Gamma_{-}] [\chi (R)] [-\chi (R)]

[1'] [ C_{1}\times {\bb Z}_{2}] cf. 1
[21'] [C_{2}\times {\bb Z}_{2}] cf. 2
[m1'] [C_{2}\times {\bb Z}_{2}] cf. m
[2221'] [D_{2}\times {\bb Z}_{2}] cf. 222
[2mm1'] [D_{2}\times {\bb Z}_{2}] cf. [2mm]
[41'] [C_{4}\times {\bb Z}_{2}] cf. 4
[\bar{4}1'] [C_{4}\times {\bb Z}_{2}] cf. [\bar{4}]
[4mm1'] [D_{4}\times{\bb Z}_{2}] cf. [4mm]
[4221'] [D_{4}\times{\bb Z}_{2}] cf. 422
[\bar{4}2m1'] [D_{4}\times{\bb Z}_{2}] cf. [\bar{4}2m]
[31'] [C_{3}\times {\bb Z}_{2}] cf. 3
[321'] [D_{3}\times{\bb Z}_{2}] cf. 32
[\bar{3}1'] [C_{6}\times{\bb Z}_{2}] cf. [\bar{3}]
[3m1'] [D_{3}\times{\bb Z}_{2}] cf. [3m]
[6mm1'] [D_{6}\times{\bb Z}_{2}] cf. [6mm]
[61'] [C_{6}\times{\bb Z}_{2}] cf. 6
[\bar{6}1'] [C_{6}\times {\bb Z}_{2}] cf. [\bar{6}]
[6221'] [D_{6}\times{\bb Z}_{2}] cf. 622
[\bar{6}2m1'] [D_{6}\times{\bb Z}_{2}] cf. [\bar{6}2m]
[231'] [T\times{\bb Z}_{2}] cf. 23
[4321'] [O\times{\bb Z}_{2}] cf. 432
[\bar{4}3m1'] [O\times{\bb Z}_{2}] cf. [\bar{4}3m]

(c) With [\{E,\bar{1}\}] and [\{E,1'\}].

[K\times {\bb Z}_{2} \times {\bb Z}_{2}][R\in K][\bar{R}][R'][\bar{R}']
[ \Gamma_{g+}] [\chi (R)] [\chi (R)] [\chi (R)] [\chi (R)]
[\Gamma_{u+}] [\chi (R)] [-\chi (R)] [\chi (R)] [-\chi (R)]
[\Gamma_{g-}] [\chi (R)] [\chi (R)] [-\chi (R)] [-\chi (R)]
[\Gamma_{u-}] [\chi (R)] [-\chi (R)] [-\chi (R)] [\chi (R)]

[\bar{1}'] [C_{1}\times {\bb Z}_{2}\times {\bb Z}_{2}] cf. 1
[21'/m] [C_{2}\times {\bb Z}_{2}\times {\bb Z}_{2}] cf. 2
[4/m1'] [C_{4}\times {\bb Z}_{2}\times {\bb Z}_{2}] cf. 4
[6/m1'] [C_{6}\times {\bb Z}_{2}\times {\bb Z}_{2}] cf. 6
[mmm1'] [D_{2}\times {\bb Z}_{2}\times {\bb Z}_{2}] cf. 222
[4/mmm1'] [D_{4}\times{\bb Z}_{2}\times {\bb Z}_{2}] cf. 422
[\bar{3}m1'] [D_{6}\times{\bb Z}_{2}\times {\bb Z}_{2}] cf. [3m]
[6/mmm1'] [D_{6}\times{\bb Z}_{2}\times {\bb Z}_{2}] cf. 622
[m31'] [T\times{\bb Z}_{2}\times {\bb Z}_{2}] cf. 23
[m(\bar{3})m1'] [O\times{\bb Z}_{2}\times {\bb Z}_{2}] cf. 432