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

© International Union of Crystallography 2006

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International Tables for Crystallography (2006). Vol. D. ch. 1.2, p. 60

Table 1.2.6.6

T. Janssen^a ^*

^a Institute 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 $[\{E,\bar{1}\}]$ .

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

	$[C_{4}\times {\bb Z}_{2}]$	cf. 4
	$[C_{6}\times {\bb Z}_{2}]$	cf. 6
	$[D_{2}\times {\bb Z}_{2}]$	cf. 222
	$[D_{4}\times{\bb Z}_{2}]$	cf. 422
	$[D_{6}\times{\bb Z}_{2}]$	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 $[\{E,1'\}]$ .

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

	$[ C_{1}\times {\bb Z}_{2}]$	cf. 1
	$[C_{2}\times {\bb Z}_{2}]$	cf. 2
	$[C_{2}\times {\bb Z}_{2}]$	cf. m
	$[D_{2}\times {\bb Z}_{2}]$	cf. 222
	$[D_{2}\times {\bb Z}_{2}]$	cf.
	$[C_{4}\times {\bb Z}_{2}]$	cf. 4
$[\bar{4}1']$	$[C_{4}\times {\bb Z}_{2}]$	cf. $[\bar{4}]$
	$[D_{4}\times{\bb Z}_{2}]$	cf.
	$[D_{4}\times{\bb Z}_{2}]$	cf. 422
$[\bar{4}2m1']$	$[D_{4}\times{\bb Z}_{2}]$	cf. $[\bar{4}2m]$
	$[C_{3}\times {\bb Z}_{2}]$	cf. 3
	$[D_{3}\times{\bb Z}_{2}]$	cf. 32
$[\bar{3}1']$	$[C_{6}\times{\bb Z}_{2}]$	cf. $[\bar{3}]$
	$[D_{3}\times{\bb Z}_{2}]$	cf.
	$[D_{6}\times{\bb Z}_{2}]$	cf .
	$[C_{6}\times{\bb Z}_{2}]$	cf. 6
$[\bar{6}1']$	$[C_{6}\times {\bb Z}_{2}]$	cf. $[\bar{6}]$
	$[D_{6}\times{\bb Z}_{2}]$	cf. 622
$[\bar{6}2m1']$	$[D_{6}\times{\bb Z}_{2}]$	cf. $[\bar{6}2m]$
	$[T\times{\bb Z}_{2}]$	cf. 23
	$[O\times{\bb Z}_{2}]$	cf. 432
$[\bar{4}3m1']$	$[O\times{\bb Z}_{2}]$	cf. $[\bar{4}3m]$

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

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

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

© International Union of Crystallography 2006

International Tables for Crystallography (2006). Vol. D. ch. 1.2, p. 60

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