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

International Tables for Crystallography (2013). Vol. D, ch. 3.4, pp. 498-502

Table 3.4.2.7 

V. Janoveca* and J. Přívratskáb

aInstitute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, CZ-18221 Prague 8, Czech Republic, and bDepartment of Mathematics and Didactics of Mathematics, Technical University of Liberec, Hálkova 6, 461 17 Liberec 1, Czech Republic
Correspondence e-mail:  janovec@fzu.cz

Table 3.4.2.7| top | pdf |
Group–subgroup symmetry descents [G \supset F_1]

G: point-group symmetry of parent phase; [F_1]: point-group symmetry of single-domain state [{\bf S}_1]; [\Gamma_{\eta} ]: representation of G; [N_{G}(F_1)]: normalizer of [F_1] in G; [K_G(F_1, g_{1j})]: twinning groups, [g_{1j}\in G]; n: number of principal single-domain states; [d_F]: number of principal domain states with the same symmetry; [n_e]: number of ferroelectric single-domain states; [n_a]: number of ferroelastic single-domain states.

G[F_1][\Gamma_{\eta}][N_{G}(F_1)][K_G(F_1, g_{1j})]n[d_F ][n_e ][n_a ]
[ {\bar {\bf 1}}] 1 [A_u] [\bar1] [\bar1^{\star}] 2 2 2 1
[{\bf 2}_{\bi u}] 1 B [2_u] [2_u^\star] 2 2 2 2
[{\bi m_u}] 1 [A{^\prime}{^\prime}] [m_u] [m_u^\star] 2 2 2 2
[{\bf 2}_{\bi u}/{\bi m_u} ] [m_u] [B_u] [2_u/m_u] [2_u^\star/m_u] 2 2 2 1
[2_u] [A_u] [2_u/m_u] [2_u/m_u^\star] 2 2 2 1
[\bar 1 ] [B_g ] [2_u/m_u] [2_u^\star/m_u^\star] 2 2 0 2
1 Reducible [2_u/m_u] [m_u^{\star}], [ 2_u^{\star}], [\bar 1^{\star}] 4 4 4 2
[{\bf 2}_{\bi x}{\bf 2}_{\bi y}{\bf 2}_{\bi z} ] [2_z] [B_{1g} ] [2_x2_y2_z ] [2_x^\star2_y^\star2_z ] 2 2 2 2
[2_x] [B_{3g} ] [2_x2_y2_z] [2_x2_y^\star2_z^\star ] 2 2 2 2
[2_y] [B_{2g} ] [2_x2_y2_z] [2_x^\star2_y2_z^\star] 2 2 2 2
1 Reducible [2_x2_y2_z] [2_z^{\star}], [2_x^{\star}], [2_y^{\star}] 4 4 4 4
[{\bi m_xm_y}{\bf 2}_{\bi z} ] [m_x] [B_2] [m_xm_y2_z] [m_xm_y^{\star}2_z^{\star}] 2 2 2 2
[m_y ] [B_1] [m_xm_y2_z] [m_x^{\star}m_y2_z^{\star}] 2 2 2 2
[2_z] [A_2] [m_xm_y2_z] [m_x^{\star}m_y^{\star}2_z] 2 2 1 2
1 Reducible [m_xm_y2_z] [m_x^{\star}], [m_y^{\star}], [2_z^{\star} ] 4 2 4 4
[{\bi m_xm_ym_z}] [m_xm_y2_z ] [B_{1u} ] [m_xm_ym_z] [m_xm_ym_z^\star] 2 2 2 1
[2_xm_ym_z ] [B_{3u} ] [m_xm_ym_z] [m_x^{\star}m_ym_z] 2 2 2 1
[m_x2_ym_z ] [B_{2u} ] [m_xm_ym_z] [m_xm_y^{\star}m_z] 2 2 2 1
[2_x2_y2_z ] [A_{1u} ] [m_xm_ym_z] [m_x^{\star}m_y^{\star}m_z^{\star}] 2 2 0 1
[2_z/m_z] [B_{1g} ] [m_xm_ym_z] [m_x^{\star}m_y^{\star}m_z ] 2 2 0 2
[2_x/m_x] [B_{3g} ] [m_xm_ym_z] [m_xm_y^{\star}m_z^{\star}] 2 2 0 2
[2_y/m_y] [B_{2g} ] [m_xm_ym_z] [m_x^{\star}m_ym_z^{\star}] 2 2 0 2
[m_z ] Reducible [m_xm_ym_z] [2_x^{\star}m_y^{\star}m_z], [m_x^{\star}2_y^{\star}m_z], [2_z^{\star}/m_z] 4 4 4 2
[m_x ] Reducible [m_xm_ym_z] [m_xm_y^{\star}2_z^{\star}], [m_x2_y^{\star}m_z^{\star}], [2_x^{\star}/m_x] 4 4 4 2
[m_y ] Reducible [m_xm_ym_z] [m_x^{\star}m_y2_z^{\star}], [2_x^{\star}m_ym_z^{\star}], [2_y^{\star}/m_y] 4 4 4 2
[2_z ] Reducible [m_xm_ym_z] [m_x^{\star}m_y^{\star}2_z], [2_x^{\star}2_y^{\star}2_z], [2_z/m_z^{\star}] 4 4 2 2
[2_x ] Reducible [m_xm_ym_z] [2_xm_y^{\star}m_z^{\star}], [2_x2_y^{\star}2_z^{\star}], [2_x/m_x^{\star}] 4 4 2 2
[2_y ] Reducible [m_xm_ym_z] [m_x^{\star}2_ym_z^{\star}], [2_x^{\star}2_y2_z^{\star}], [2_y/m_y^{\star}] 4 4 2 2
[\bar 1] Reducible [m_xm_ym_z] [2_z^{\star}/m_z^{\star}], [2_x^{\star}/m_x^{\star} ], [2_y^{\star}/m_y^{\star}] 4 4 0 4
1 Reducible [m_xm_ym_z] [m_z^{\star}], [m_x^{\star}], [m_y^{\star}], [2_z^{\star}], [2_x^{\star}], [2_y^{\star} ], [\bar 1^{\star}] 8 8 8 4
[{\bf 4}_{\bi z} ] [2_z ] B [4_z] [4_z^{\star} ] 2 2 1 2
1 [^1E\oplus ^2E] [4_z] [4_z, 2_z^{\star}] 4 4 4 4
[{\bar {\bf 4}}_{\bi z} ] [2_z ] B [\bar4_z ] [\bar 4_z^{\star}] 2 2 2 2
1 [^1E\oplus ^2E ] [\bar4_z ] [\bar 4_z,] [2_z^{\star}] 4 2 4 4
[{\bf 4}_{\bi z}/{\bi m_z} ] [\bar4_z] [B_u] [4_z/m_z ] [4_z^{\star}/m_z^{\star} ] 2 2 0 1
[4_z ] [A_u] [4_z/m_z ] [4_z/m_z^{\star} ] 2 2 2 1
[2_z/m_z ] [B_g] [4_z/m_z ] [4_z^{\star}/m_z ] 2 2 0 2
[m_z] [^1E_u \oplus ^2E_u] [4_z/m_z] [4_z/m_z], [2_z^{\star}/m_z] 4 4 4 2
[2_z] Reducible [4_z/m_z] [\bar 4_z^{\star}], [4_z^{\star} ], [2_z/m_z^{\star}] 4 4 2 2
[\bar 1] [^1E_g \oplus ^2E_g ] [4_z/m_z] [4_z/m_z], [2_z^{\star}/m_z^{\star} ] 4 4 0 4
1 Reducible [4_z/m_z] [\bar4_z], [4_z], [m_z^{\star} ], [2_z^{\star}], [\bar1^{\star}] 8 8 8 4
[{\bf 4}_{\bi z}{\bf 2}_{\bi x}{\bf 2}_{\bi xy} ] [4_z] [A_2] [4_z2_x2_{xy}] [4_z2_x^{\star}2_{xy}^{\star}] 2 2 2 1
[2_{x\bar{y}}2_{xy}2_z] [B_2] [4_z2_x2_{xy}] [4_z^{\star}2_x^{\star}2_{xy}] 2 2 0 2
[2_x2_y2_z ] [B_1] [4_z2_x2_{xy} ] [4_z^{\star}2_x2_{xy}^{\star}] 2 2 0 2
[2_{xy}] [(2_{x\bar{y}})] E [2_{x\bar{y}}2_{xy}2_z ] [4_z2_x2_{xy}], [2_{x\bar{y}}^{\star}2_{xy}2_z^{\star} ] 4 2 2 2
[2_z ] Reducible [4_z2_x2_{xy}] [4_z^{\star}], [2_x^{\star}2_y^{\star}2_z ], [2_{x\bar{y}}^{\star}2_{xy}^{\star}2_z] 4 4 2 2
[2_x] [(2_y)] E [2_{x\bar{y}}2_{xy}2_z] [4_z2_x2_{xy}], [2_x2_y^{\star}2_z^{\star} ] 4 2 2 2
1 E [4_z2_x2_{xy}] [4_z], [2_z^{\star}], [2_x^{\star}(2)], [2_{xy}^{\star}(2)] 8 8 8 8
[{\bf 4}_{\bi z}{\bi m}_{\bi x}{\bi m}_{\bi xy} ] [4_z ] [A_2] [4_zm_xm_{xy}] [4_zm_x^{\star}m_{xy}^{\star} ] 2 2 1 1
[m_{x\bar{y}}m_{xy}2_z] [B_2] [4_zm_xm_{xy} ] [4_z^{\star}m_x^{\star}m_{xy} ] 2 2 1 2
[m_xm_y2_z ] [B_1] [4_zm_xm_{xy} ] [4_z^{\star}m_xm_{xy}^{\star} ] 2 2 1 2
[m_{xy}] [(m_{x\bar{y}})] E [m_{x\bar{y}}m_{xy}2_z] [4_zm_xm_{xy}], [m_{x\bar{y}}^{\star}m_{xy}2_z^{\star} ] 4 2 4 4
[m_x] [(m_y)] E [m_xm_y2_z ] [4_zm_xm_{xy}], [m_xm_y^{\star}2_z^{\star} ] 4 2 4 4
[2_z] Reducible [4_zm_xm_{xy} ] [4_z^{\star}], [m_x^{\star}m_y^{\star}2_z ], [m_{x\bar{y}}^{\star}m_{xy}^{\star}2_z] 4 4 2 2
1 E [4_zm_xm_{xy} ] [4_z], [m_x^{\star}(2)], [m_{xy}^{\star}(2)], [2_z^{\star}] 8 8 8 8
[{\bar {\bf 4}}_{\bi z}{\bf 2}_{\bi x}{\bi m_{xy}} ] [\bar4_z] [A_2] [\bar4_z2_xm_{xy}] [\bar4_z2_x^{\star}m_{xy}^{\star}] 2 2 0 1
[m_{x\bar{y}}m_{xy}2_z] [B_2] [\bar4_z2_xm_{xy}] [\bar4_z^{\star}2_x^{\star}m_{xy}] 2 2 2 2
[2_x2_y2_z ] [B_1] [\bar4_z2_xm_{xy}] [\bar4_z^{\star}2_xm_{xy}^{\star}] 2 2 0 2
[m_{xy}] [(m_{x\bar{y}})] E [m_{x\bar{y}}m_{xy}2_z] [\bar4_z2_xm_{xy}], [m_{x\bar{y}}^{\star}m_{xy}2_z^{\star} ] 4 2 4 4
[2_z ] Reducible [\bar4_z2_xm_{xy}] [\bar4_z^{\star}], [m_{x\bar{y}}^{\star}m_{xy}^{\star}2_z ], [2_x^{\star}2_y^{\star}2_z] 4 4 2 2
[2_x ] [(2_y) ] E [2_x2_y2_z ] [\bar4_z2_xm_{xy}], [2_x2_y^{\star}2_z^{\star} ] 4 2 4 4
1 E [\bar4_z2_xm_{xy}] [\bar4_z], [m_{xy}^{\star}(2)], [2_z^{\star}], [2_x^{\star}(2)] 8 8 8 8
[\bar4_zm_x2_{xy}] [\bar4_z] [A_2] [\bar4_zm_x2_{xy}] [\bar4_zm_x^{\star}2_{xy}^{\star}] 2 2 0 1
[m_xm_y2_z ] [B_2] [\bar4_zm_x2_{xy}] [\bar4_z^{\star}m_x2_{xy}^{\star}] 2 2 2 2
[2_{x\bar{y}}2_{xy}2_z] [B_1] [\bar4_zm_x2_{xy}] [\bar4_z^{\star}m_x^{\star}2_{xy}] 2 2 0 2
[m_x] [(m_y)] E [m_xm_y2_z ] [\bar4_zm_x2_{xy}], [m_xm_y^{\star}2_z^{\star} ] 4 2 4 4
[2_{xy}] [(2_{x\bar{y}})] E [2_{x\bar{y}}2_{xy}2_z] [\bar4_zm_x2_{xy}], [2_{x\bar{y}}^{\star}2_{xy}2_z^{\star} ] 4 2 4 4
[2_z ] Reducible [\bar4_zm_x2_{xy}] [\bar4_z^{\star} ], [m_x^{\star}m_y^{\star}2_z ], [2_{x\bar{y}}^{\star}2_{xy}^{\star}2_z] 4 4 2 2
1 E [\bar4_zm_x2_{xy}] [\bar4_z], [m_x^{\star}(2)], [2_{xy}^{\star}(2)], [2_z^{\star}] 8 8 8 8
[{\bf 4}_{\bi z}/{\bi m_zm_xm_{xy}} ] [\bar4_zm_x2_{xy}] [B_{2u}] [4_z/m_zm_xm_{xy} ] [4_z^{\star}/m_z^{\star}m_xm_{xy}^{\star} ] 2 2 0 1
[\bar4_z2_xm_{xy} ] [B_{1u} ] [4_z/m_zm_xm_{xy} ] [4_z^{\star}/m_z^{\star}m_x^{\star}m_{xy} ] 2 2 0 1
[4_zm_xm_{xy} ] [A_{2u} ] [4_z/m_zm_xm_{xy} ] [4_z^{\star}/m_z^{\star}m_xm_{xy}] 2 2 2 1
[4_z2_x2_{xy} ] [A_{1u} ] [4_z/m_zm_xm_{xy} ] [4_z^{\star}/m_z^{\star}m_x^{\star}m_{xy} ] 2 2 0 1
[4_z/m_z ] [A_{2g} ] [4_z/m_zm_xm_{xy} ] [4_z^{\star}/m_zm_x^{\star}m_{xy}^{\star} ] 2 2 0 1
[\bar4_z ] Reducible [4_z/m_zm_xm_{xy} ] [\bar4_z2_x^{\star}m_{xy}^{\star}], [\bar4_zm_x^{\star}2_{xy}^{\star}], [4_z^{\star}/m_z^{\star}] 4 4 0 1
[4_z] Reducible [4_z/m_zm_xm_{xy} ] [4_zm_x^{\star}m_{xy}^{\star} ], [4_z2_x^{\star}2_{xy}^{\star}], [4_z/m_z^{\star}] 4 4 2 1
[m_{x\bar{y}}m_{xy}m_z ] [B_{2g} ] [4_z/m_zm_xm_{xy}] [4_z^{\star}/m_zm_x^{\star}m_{xy}] 2 2 0 2
[m_xm_ym_z] [B_{1g} ] [m_xm_ym_z ] [4_z^{\star}/m_zm_xm_{xy}^{\star}] 2 2 0 2
[2_{x\bar{y}}m_{xy}m_z] [(m_{x\bar{y}}2_{xy}m_z)] [E_u] [m_{x\bar{y}}m_{xy}m_z ] [4_z/m_zm_xm_{xy}], [m_{x\bar{y}}^{\star}m_{xy}m_z ] 4 2 4 2
[2_xm_ym_z] [(m_x2_ym_z)] [E_u] [m_xm_ym_z] [4_z/m_zm_xm_{xy}], [m_x^{\star}m_ym_z ] 4 2 4 2
[m_{x\bar{y}}m_{xy}2_z ] Reducible [4_z/m_zm_xm_{xy}] [\bar4_z^{\star}2_x^{\star}m_{xy}], [4_z^{\star}m_x^{\star}m_{xy}], [m_{x\bar{y}}m_{xy}m_z^{\star} ] 4 4 2 2
[m_xm_y2_z] Reducible [4_z/m_zm_xm_{xy}] [\bar4_z^{\star}m_x2_{xy}^{\star}], [4_z^{\star}m_xm_{xy}^{\star}], [m_xm_ym_z^{\star} ] 4 4 2 2
[2_{x\bar{y}}2_{xy}2_z ] Reducible [4_z/m_zm_xm_{xy}] [\bar4_z^{\star}m_x^{\star}2_{xy}], [4_z^{\star}2_x^{\star}2_{xy}], [m_{x\bar{y}}^{\star}m_{xy}^{\star}m_z^{\star} ] 4 4 0 2
[2_x2_y2_z] Reducible [4_z/m_zm_xm_{xy} ] [\bar4_z^{\star}2_xm_{xy}^{\star}], [4_z^{\star}2_x2_{xy}^{\star}], [m_x^{\star}m_y^{\star}m_z^{\star}] 4 4 0 2
[2_{xy}/m_{xy}] [(2_{x\bar{y}}/m_{x\bar{y}})] [E_g] [m_{x\bar{y}}m_{xy}m_z ] [4_z/m_zm_xm_{xy}], [m_{x\bar{y}}^{\star}m_{xy}m_z^{\star} ] 4 2 0 4
[2_z/m_z ] Reducible [4_z/m_zm_xm_{xy}] [4_z^{\star}/m_z], [m_{x\bar{y}}^{\star}m_{xy}^{\star}m_z ], [m_x^{\star}m_y^{\star}m_z ] 4 4 0 4
[2_x/m_x] [(2_y/m_y)] [E_g] [m_xm_ym_z] [4_z/m_zm_xm_{xy}], [m_xm_y^{\star}m_z^{\star} ] 4 2 0 4
[m_{xy} (m_{x \bar y})] Reducible [m_{x\bar{y}}m_{xy}m_z ] [\bar4_z2_xm_{xy}], [4_zm_xm_{xy} ], [2_{x\bar{y}}^{\star}m_{xy}m_z^{\star}], [m_{x\bar{y}}^{\star}m_{xy}2_z^{\star} ], [2_{xy}^{\star}/m_{xy}] 8 4 8 4
[m_z ] [E_u] [4_z/m_zm_xm_{xy} ] [4_z/m_z], [2_{x\bar{y}}^{\star}m_{xy}^{\star}m_z(2) ], [2_x^{\star}m_y^{\star}m_z(2)], [2_z^{\star}/m_z ] 8 8 8 4
[m_x] [(m_y) ] Reducible [m_xm_ym_z] [\bar4_zm_x2_{xy}], [4_zm_xm_{xy} ], [m_xm_y^{\star}2_z^{\star}], [m_x2_y^{\star}m_z^{\star}], [2_x^{\star}/m_x] 8 4 8 4
[2_{xy}] [(2_{x\bar{y}})] Reducible [m_{x\bar{y}}m_{xy}m_z ] [\bar4_zm_x2_{xy}], [4_z2_x2_{xy} ], [m_{x\bar{y}}^{\star}2_{xy}m_z^{\star}], [2_{x\bar{y}}^{\star}2_{xy}2_z^{\star} ], [2_{xy}/m_{xy}^{\star}] 8 4 8 4
[2_z] Reducible [4_z/m_zm_xm_{xy}] [\bar4_z^{\star}], [4_z^{\star} ], [m_x^{\star}m_y^{\star}2_z], [m_{x\bar{y}}^{\star}m_{xy}^{\star}2_z ], [2_x^{\star}2_y^{\star}2_z], [2_{x\bar{y}}^{\star}2_{xy}^{\star}2_z ], [2_z/m_z^{\star}] 8 8 2 4
[2_x] [(2_y)] Reducible [m_xm_ym_z] [\bar4_z2_xm_{xy}], [4_z2_x2_{xy} ], [2_xm_y^{\star}m_z^{\star}], [2_x2_y^{\star}2_z^{\star}], [2_x/m_x^{\star}] 8 4 4 4
[\bar1] [E_g] [4_z/m_zm_xm_{xy} ] [4_z/m_z], [2_{xy}^{\star}/m_{xy}^{\star}(2) ], [2_z^{\star}/m_z^{\star}], [2_x^{\star}/m_x^{\star}(2)] 8 8 0 8
1 Reducible [4_z/m_zm_xm_{xy}] [\bar4_z], [4_z], [m_{xy}^{\star}(2) ], [m_z^{\star}], [m_x^{\star}(2)], [2_{xy}^{\star}(2) ], [2_z^{\star}], [2_x^{\star}(2)], [\bar1^{\star}] 16 16 16 8
[{\bf 3}_{\bi z} ] 1 E [3_z ] [3_z ] 3 3 3 3
[{\bar {\bf 3}}_{\bi z} ] [3_z ] [A_u] [\bar3_z ] [\bar 3_z^{\star} ] 2 2 2 1
[\bar 1 ] [E_g] [\bar3_z ] [\bar 3_z] 3 3 0 3
1 [E_u] [\bar3_z ] [\bar 3_z], [3_z], [\bar 1^{\star} ] 6 6 6 3
[{\bf 3}_{\bi z}{\bf 2}_{\bi x} ] [3_z] [A_2] [3_z2_x] [3_z2_x^{\star}] 2 2 2 1
[2_x] [(2_{x^{\prime}}], [2_{x^{{\prime}{\prime}}})] E [2_x ] [3_z2_x ] 3 1 3 3
1 E [3_z2_x] [3_z, 2_x^{\star}(3) ] 6 6 6 6
[3_z2_y ] [3_z] [A_2] [3_z2_y] [3_z2_y^{\star}] 2 2 2 1
[2_y] [(2_{y^{\prime}}], [2_{y^{{\prime}{\prime}}})] E [2_y] [3_z2_y ] 3 1 3 3
1 E [3_z2_y] [3_z], [2_y^{\star}(3)] 6 6 6 6
[{\bf 3}_{\bi z}{\bi m_x} ] [3_z] [A_2] [3_zm_x] [3_zm_x^{\star}] 2 2 1 1
[m_x] [(m_{x^\prime}], [m_{x{^\prime}{^\prime}})] E [m_x ] [3_zm_x ] 3 1 3 3
1 E [3_zm_x] [3_z], [m_x^{\star}(3)] 6 6 6 6
[3_zm_y] [3_z] [A_2] [3_zm_y] [3_zm_y^{\star}] 2 2 1 1
[m_y ] [(m_{y{^\prime}}], [m_{y{^\prime}{^\prime}})] E [m_y] [3_zm_y ] 3 1 3 3
1 E [3_zm_y] [3_z], [m_y^{\star}(3)] 6 6 6 6
[{\bar {\bf 3}}_{\bi z}{\bi m_x} ] [3_zm_x ] [A_{2u} ] [\bar3_zm_x ] [\bar3_z^{\star}m_x ] 2 2 2 1
[3_z2_x ] [A_{1u} ] [\bar3_zm_x ] [\bar3_z^{\star}m_x^{\star}] 2 2 0 1
[\bar 3_z ] [A_{2g} ] [\bar3_zm_x ] [\bar3_zm_x^{\star} ] 2 2 0 1
[3_z ] Reducible [\bar3_zm_x] [3_zm_x^{\star}], [3_z2_x^{\star} ], [\bar 3_z^{\star} ] 4 4 2 1
[2_x/m_x] [(2_{x^\prime}/m_{x^\prime} ], [2_{x{^\prime}{^\prime}}/m_{x{^\prime}{^\prime}})] [E_g] [2_x/m_x] [\bar3_zm_x ] 3 1 0 3
[m_x] [(m_{x{^\prime}}], [m_{x{^\prime}{^\prime}})] [E_u] [2_x/m_x] [\bar3_zm_x], [3_zm_x], [2_x^{\star}/m_x(3)] 6 2 6 3
[2_x ] [(2_{x{^\prime}}], [2_{x{^\prime}{^\prime}})] [E_u] [2_x/m_x] [\bar3_zm_x], [3_z2_x], [2_x/m_x^{\star}(3) ] 6 2 6 3
[\bar 1] [E_g] [\bar3_zm_x] [\bar 3_z], [2_x^{\star}/m_x^{\star}(3) ] 6 6 0 6
1 [E_u] [\bar3_zm_x] [\bar 3_z], [3_z], [m_x^{\star}(3) ], [2_x^{\star}(3)], [\bar 1^{\star} ] 12 12 12 6
[\bar3_zm_y] [3_zm_y] [A_{2u}] [\bar3_zm_y] [\bar3_z^{\star}m_y] 2 2 2 1
[3_z2_y] [A_{1u}] [\bar3_zm_y] [\bar3_z^{\star}m_y^{\star}] 2 2 0 1
[\bar 3_z] [A_{2g}] [\bar3_zm_y] [\bar3_zm_y^{\star}] 2 2 0 1
[3_z] Reducible [\bar3_zm_y] [3_zm_y^{\star}], [3_z2_y^{\star} ], [\bar 3_z^{\star}] 4 4 0 1
[2_y/m_y] [(2_{y{^\prime}}/m_{y{^\prime}} ], [2_{y{^\prime}{^\prime}}/m_{y{^\prime}{^\prime}})] [E_g] [2_y/m_y] [\bar3_zm_y ] 3 1 2 1
[m_y] [(m_{y{^\prime}}], [m_{y{^\prime}{^\prime}})] [E_u] [2_y/m_y] [\bar3_zm_y], [3_zm_y], [2_y^{\star}/m_y(3)] 6 2 0 3
[2_y ] [(2_{y{^\prime}}], [2_{y{^\prime}{^\prime}}) ] [E_u] [2_y/m_y] [\bar3_zm_y], [3_z2_y], [2_y/m_y^{\star}(3) ] 6 2 6 3
[\bar 1] [E_g] [\bar3_zm_y] [\bar 3_z], [2_y^{\star}/m_y^{\star}(3) ] 6 6 0 3
1 [E_u] [\bar3_zm_y] [\bar 3_z], [3_z], [m_y^{\star}(3) ], [2_y^{\star}(3)], [\bar 1^{\star}] 12 12 12 6
[{\bf 6}_{\bi z} ] [3_z] B [6_z ] [6_z^{\star}] 2 2 1 1
[2_z] [E_2] [6_z] [6_z ] 3 3 1 3
1 [E_1] [6_z] [6_z], [3_z], [2_z^{\star} ] 6 6 6 6
[{\bar{\bf 6}}_{\bi z} ] [3_z] [A{^\prime}{^\prime}] [\bar6_z] [\bar 6_z^{\star}] 2 2 2 1
[m_z] [E{^\prime}] [\bar6_z] [\bar 6_z] 3 2 3 3
1 [E{^\prime}{^\prime}] [\bar6_z] [\bar 6_z ], [3_z], [m_z^{\star} ] 6 6 6 6
[{\bf 6}_{\bi z}/{\bi m_z} ] [\bar 6_z] [B_u ] [6_z/m_z] [6_z^{\star}/m_z] 2 2 0 1
[6_z ] [A_u ] [6_z/m_z] [6_z/m_z^{\star}] 2 2 2 1
[\bar 3_z ] [B_g ] [6_z/m_z] [6_z^{\star}/m_z^{\star} ] 2 2 0 1
[3_z ] Reducible [6_z/m_z] [\bar 6_z^{\star}], [6_z^{\star} ], [\bar 3_z^{\star}] 4 4 2 1
[2_z/m_z] [E_{2g} ] [6_z/m_z] [6_z/m_z] 3 3 0 3
[m_z ] [E_{1u} ] [6_z/m_z] [6_z/m_z], [\bar 6_z], [2_z^{\star}/m_z ] 6 6 6 3
[2_z ] [E_{2u} ] [6_z/m_z] [6_z/m_z], [6_z], [2_z/m_z^{\star} ] 6 6 2 3
[\bar 1 ] [E_{1g} ] [6_z/m_z] [6_z/m_z], [\bar 3_z], [2_z^{\star}/m_z^{\star} ] 6 6 0 6
1 Reducible [6_z/m_z] [\bar 6_z], [6_z], [\bar 3_z ], [3_z], [m_z^{\star}], [2_z^{\star}], [\bar 1^{\star} ] 12 12 12 6
[{\bf 6}_{\bi z}{\bf 2}_{\bi x}{\bf 2}_{\bi y}] [6_z] [A_2 ] [6_z2_x2_y] [6_z2_x^{\star}2_y^{\star}] 2 2 2 1
[3_z2_x] [B_1 ] [6_z2_x2_y ] [6_z^{\star}2_x2_y^{\star}] 2 2 0 1
[3_z2_y] [B_2 ] [6_z2_x2_y ] [6_z^{\star}2_x^{\star}2_y] 2 2 0 1
[3_z ] Reducible [6_z2_x2_y] [6_z^{\star}], [3_z2_x^{\star} ], [3_z2_y^{\star} ] 4 4 2 1
[2_x2_y2_z] [(2_{x{^\prime}}2_{y{^\prime}}2_z ], [2_{x{^\prime}{^\prime}}2_{y{^\prime}{^\prime}}2_z)] [E_2] [2_x2_y2_z] [6_z2_x2_y ] 3 1 0 3
[2_z ] [E_2] [6_z 2_x2_y] [6_z], [2_x^{\star}2_y^{\star}2_z(3) ] 6 6 2 6
[2_x] [(2_{x{^\prime}}], [2_{x{^\prime}{^\prime}})] [E_1] [2_x2_y2_z] [6_z2_x2_y], [3_z2_x], [2_x2_y^{\star}2_z^{\star}] 6 2 6 6
[2_y] [(2_{y{^\prime}}], [2_{y{^\prime}{^\prime}})] [E_1] [2_x2_y2_z] [6_z2_x2_y], [3_z2_y], [2_x^{\star}2_y2_z^{\star} ] 6 2 6 6
1 [E_1] [6_z2_x2_y] [6_z], [3_z], [2_z^{\star} ], [2_x^{\star}(3)], [2_y^{\star}(3)] 12 12 12 12
[{\bf 6}_{\bi z}{\bi m}_{\bi x}{\bi m}_{\bi y} ] [6_z] [A_2] [6_zm_xm_y] [6_zm_x^{\star}m_y^{\star} ] 2 2 1 1
[3_zm_x] [B_2] [6_zm_xm_y] [6_z^{\star}m_xm_y^{\star}] 2 2 1 1
[3_zm_y] [B_1] [6_zm_xm_y] [6_z^{\star}m_x^{\star}m_y] 2 2 1 1
[3_z ] Reducible [6_zm_xm_y] [6_z^{\star}], [3_zm_x^{\star} ], [3_zm_y^{\star}] 4 4 1 1
[m_xm_y2_z] [(m_{x{^\prime}}m_{y{^\prime}}2_z ], [m_{x{^\prime}{^\prime}}m_{y{^\prime}{^\prime}}2_z)] [E_2] [m_xm_y2_z] [6_zm_xm_y] 3 1 1 3
[m_x] [(m_{x{^\prime}}], [m_{x{^\prime}{^\prime}})] [E_1] [m_xm_y2_z] [6_zm_xm_y], [3_zm_x], [m_xm_y^{\star}2_z^{\star}] 6 2 6 6
[m_y ] [(m_{y{^\prime}}], [m_{y{^\prime}{^\prime}})] [E_1] [m_xm_y2_z] [6_zm_xm_y], [3_zm_y], [m_x^{\star}m_y2_z^{\star}] 6 2 6 6
[2_z ] [E_2] [6_zm_xm_y] [6_z], [m_x^{\star}m_y^{\star}2_z(3) ] 6 6 1 6
1 [E_1] [6_zm_xm_y] [6_z], [3_z], [2_z^{\star} ], [m_x^{\star}(3)], [m_y^{\star}(3)] 12 12 12 12
[{\bar {\bf 6}}_{\bi z}{\bi m_x}{\bf 2}_{\bi y} ] [\bar 6_z ] [A_2{^\prime} ] [\bar6_zm_x2_y] [\bar6_zm_x^{\star}2_y^{\star}] 2 2 0 1
[3_zm_x ] [A_2{^\prime}{^\prime}] [\bar6_zm_x2_y] [\bar6_z^{\star}m_x2_y^{\star} ] 2 2 2 1
[3_z2_y ] [A_1{^\prime}] [\bar6_zm_x2_y] [\bar6_z^{\star}m_x^{\star}2_y ] 2 2 0 1
[3_z ] Reducible [\bar6_zm_x2_y] [\bar 6_z^{\star} ], [3_zm_x^{\star} ], [3_z2_y^{\star}] 4 4 2 1
[m_x2_ym_z] [(m_{x{^\prime}}2_{y{^\prime}}m_z ], [m_{x{^\prime}{^\prime}}2_{y{^\prime}{^\prime}}m_z)] [E{^\prime}] [m_x2_ym_z] [\bar6_zm_x2_y] 3 1 3 3
[m_z ] [E{^\prime}] [\bar6_zm_x2_y] [\bar6_z, m_x^{\star}2_y^{\star}m_z(3) ] 6 6 6 6
[m_x] [(m_{x{^\prime}}], [m_{x{^\prime}{^\prime}})] [E{^\prime}{^\prime}] [m_y2_ym_z] [\bar6_zm_x2_y], [3_zm_x], [m_x2_y^{\star}m_z^{\star}] 6 2 6 6
[2_y] [(2_{y{^\prime}}], [2_{y{^\prime}{^\prime}})] [E{^\prime}{^\prime}] [m_x2_ym_z] [\bar6_zm_x2_y], [3_z2_y], [m_x^{\star}2_ym_z^{\star}] 6 2 3 6
1 [E{^\prime}{^\prime}] [\bar6_zm_x2_y] [\bar 6_z], [3_z], [m_z^{\star} ], [m_x^{\star}(3)], [2_y^{\star}(3)] 12 12 12 12
[\bar 6_z2_xm_y ] [\bar 6_z ] [A_2{^\prime} ] [\bar6_z2_xm_y] [\bar6_z2_x^{\star}m_y^{\star} ] 2 2 0 1
[3_zm_y] [A_2{^\prime} ] [\bar6_z2_xm_y] [\bar6_z^{\star}2_x^{\star}m_y] 2 2 2 1
[3_z2_x] [A_1{^\prime}{^\prime}] [\bar6_z2_xm_y ] [\bar6_z^{\star}2_xm_y^{\star} ] 2 2 0 1
[3_z] Reducible [\bar6_z2_xm_y ] [\bar 6_z^{\star}], [3_zm_y^{\star} ], [3_z2_x^{\star}] 4 4 2 1
[2_xm_ym_z] [(2_{x{^\prime}}m_{y{^\prime}}m_z ], [2_{x{^\prime}{^\prime}}m_{y{^\prime}{^\prime}}m_z)] [E{^\prime}] [m_x2_ym_z] [\bar6_z2_xm_y] 3 1 3 3
[m_z] [E{^\prime}] [\bar6_z2_xm_y ] [\bar6_z], [2_x^{\star}m_y^{\star}m_z(3) ] 6 6 6 6
[m_y] [(m_{y{^\prime}}], [m_{y{^\prime}{^\prime}})] [E{^\prime}{^\prime}] [m_x2_ym_z] [\bar 6_z2_xm_y], [3_zm_y], [2_x^{\star}m_ym_z^{\star}] 6 2 6 6
[2_x] [(2_{x{^\prime}}], [2_{x{^\prime}{^\prime}})] [E{^\prime}{^\prime}] [m_x2_ym_z] [\bar 6_z2_xm_y], [3_z2_x], [2_xm_y^{\star}m_z^{\star}] 6 2 3 6
1 [E{^\prime}{^\prime}] [\bar6_z2_xm_y ] [\bar 6_z], [3_z], [m_z^{\star} ], [m_y^{\star}(3)], [2_x^{\star}(3)] 12 12 12 12
[{\bf 6}_{\bi z}/{\bi m_zm_xm_y} ] [\bar 6_zm_x2_y] [B_{2u}] [6_z/m_zm_xm_y] [6_z^{\star}/m_zm_xm_y^{\star}] 2 2 0 1
[\bar 6_z2_xm_y] [B_{1u} ] [6_z/m_zm_xm_y] [6_z^{\star}/m_zm_x^{\star}m_y] 2 2 0 1
[6_zm_xm_y] [A_{2u} ] [6_z/m_zm_xm_y] [6_z/m_z^{\star}m_xm_y ] 2 2 2 1
[6_z2_x2_y] [A_{1u} ] [6_z/m_zm_xm_y] [6_z/m_z^{\star}m_x^{\star}m_y^{\star} ] 2 2 0 1
[6_z/m_z ] [A_{2g} ] [6_z/m_zm_xm_y] [6_z/m_zm_x^{\star}m_y^{\star}] 2 2 0 1
[\bar 6_z] Reducible [6_z/m_zm_xm_y] [\bar 6_zm_x^{\star}2_y^{\star}], [\bar6_z2_x^{\star}m_y^{\star} ], [6_z^{\star}/m_z ] 4 4 0 1
[6_z] Reducible [6_z/m_zm_xm_y] [6_zm_x^{\star}m_y^{\star}], [6_z2_x^{\star}2_y^{\star}], [6_z/m_z^{\star}] 4 4 2 1
[\bar 3_zm_x] [B_{1g} ] [6_z/m_zm_xm_y] [6_z^{\star}/m_z^{\star}m_xm_y^{\star} ] 2 2 0 1
[\bar 3_zm_y] [B_{2g}] [6_z/m_zm_xm_y] [6_z^{\star}/m_z^{\star}m_x^{\star}m_y ] 2 2 0 1
[3_zm_x] Reducible [6_z/m_zm_xm_y] [\bar 6_z^{\star}m_x2_y^{\star}], [6_z^{\star}m_xm_y^{\star}], [\bar 3_z^{\star}m_x ] 4 4 2 1
[3_zm_y] Reducible [6_z/m_zm_xm_y] [\bar 6_z^{\star}2_x^{\star}m_y], [6_z^{\star}m_x^{\star}m_y], [\bar 3_z^{\star}m_y] 4 4 2 1
[3_z2_x] Reducible [6_z/m_zm_xm_y] [\bar 6_z^{\star}2_xm_y^{\star}], [6_z^{\star}2_x2_y^{\star}], [\bar 3_z^{\star}m_x^{\star} ] 4 4 0 1
[3_z2_y] Reducible [6_z/m_zm_xm_y] [\bar 6_z^{\star}m_x^{\star}2_y], [6_z^{\star}2_x^{\star}2_y], [\bar 3_z^{\star}m_y^{\star}] 4 4 0 1
[\bar 3_z] Reducible [6_z/m_zm_xm_y] [6_z^{\star}/m_z^{\star}], [\bar 3_zm_x^{\star} ], [\bar 3_zm_y^{\star}] 4 4 0 1
[3_z] Reducible [6_z/m_zm_xm_y] [\bar 6_z^{\star}], [6_z^{\star} ], [3_zm_x^{\star}], [3_zm_y^{\star}], [3_z2_x^{\star} ], [3_z2_y^{\star}], [\bar 3_z^{\star}] 8 8 2 1
[m_xm_ym_z] [(m_{x{^\prime}}m_{y{^\prime}}m_z ], [m_{x{^\prime}{^\prime}}m_{y{^\prime}{^\prime}}m_z)] [E_{2g} ] [m_xm_ym_z ] [6_z/m_zm_xm_y] 3 1 0 3
[m_xm_y2_z ] [(m_{x{^\prime}}m_{y{^\prime}}2_z ], [m_{x{^\prime}{^\prime}}m_{y{^\prime}{^\prime}}2_z)] [E_{2u}] [m_xm_ym_z] [6_z/m_zm_xm_y], [6_zm_xm_y], [m_xm_ym_z^{\star}] 6 2 2 3
[2_xm_ym_z] [(2_{x{^\prime}}m_{y{^\prime}}m_z ], [2_{x{^\prime}{^\prime}}m_{y{^\prime}{^\prime}}m_z)] [E_{1u} ] [m_xm_ym_z] [6_z/m_z m_xm_y], [\bar 6_z2_xm_y ], [m_x^{\star}m_ym_z] 6 2 6 3
[m_x2_ym_z] [(m_{x{^\prime}}2_{y{^\prime}}m_z ], [m_{x{^\prime}{^\prime}}2_{y{^\prime}{^\prime}}m_z)] [E_{1u}] [m_xm_ym_z] [6_z/m_z m_xm_y], [\bar 6_zm_x2_y ], [m_xm_y^{\star}m_z] 6 2 6 3
[2_x2_y2_z] [(2_{x{^\prime}}2_{y{^\prime}}2_z ], [2_{x{^\prime}{^\prime}}2_{y{^\prime}{^\prime}}2_z)] [E_{2u}] [m_xm_ym_z ] [6_z/m_zm_xm_y], [6_z2_x2_y], [m_x^{\star}m_y^{\star}m_z^{\star}] 6 6 0 3
[2_z/m_z] [E_{2g}] [6_z/m_zm_xm_y] [6_z/m_z], [m_x^{\star}m_y^{\star}m_z(3) ] 6 6 0 6
[2_x/m_x] [(2_{x{^\prime}}/m_{x{^\prime}} ], [2_{x{^\prime}{^\prime}}/m_{x{^\prime}{^\prime}})] [E_{1g}] [m_xm_ym_z] [6_z/m_zm_xm_y], [\bar 3_zm_x], [m_xm_y^{\star}m_z^{\star} ] 6 2 0 6
[2_y/m_y] [(2_{y{^\prime}}/m_{y{^\prime}} ], [2_{y{^\prime}{^\prime}}/m_{y{^\prime}{^\prime}})] [E_{1g}] [m_xm_ym_z ] [6_z/m_zm_xm_y], [\bar 3m_y], [m_x^{\star}m_ym_z^{\star} ] 6 2 0 6
[m_z] [E_{1u}] [6_z/m_zm_xm_y] [6_z/m_z], [\bar 6_z], [2_x^{\star}m_y^{\star}m_z], [m_x^{\star}2_y^{\star}m_z], [2_z^{\star}/m_z ] 12 12 12 6
[m_x] [(m_{x{^\prime}}], [m_{x{^\prime}{^\prime}})] Reducible [m_xm_ym_z ] [\bar 6_zm_x2_y], [6_zm_xm_y], [\bar 3_zm_x], [3_zm_x], [m_xm_y^{\star}2_z^{\star}], [m_x2_y^{\star}m_z^{\star}], [ 2_x^{\star}/m_x] 12 4 12 6
[m_y] [(m_{y{^\prime}}], [m_{y{^\prime}{^\prime}})] Reducible [m_xm_ym_z] [\bar 6_z2_xm_y], [6_zm_xm_y], [\bar 3_zm_y], [3_zm_y], [m_x^{\star}m_y2_z^{\star}], [2_x^{\star}m_ym_z^{\star}], [2_y^{\star}/m_y] 12 4 12 6
[2_z] [E_{2u}] [6_z/m_zm_xm_y ] [6_z/m_z], [6_z], [m_x^{\star}m_y^{\star}2_z (3) ], [2_x^{\star}2_y^{\star}2_z(3)], [2_z/m_z^{\star}] 12 12 2 6
[2_x ] [(2_{x{^\prime}}], [2_{x{^\prime}{^\prime}})] Reducible [m_xm_ym_z] [\bar 6_z2_xm_y], [6_z2_x2_y], [\bar 3_zm_x], [3_z2_x], [2_xm_y^{\star}m_z^{\star}], [2_x2_y^{\star}2_z^{\star}], [2_x/m_x^{\star}] 12 4 6 6
[2_y] [(2_{y{^\prime}}], [2_{y{^\prime}{^\prime}})] Reducible [m_xm_ym_z] [\bar 6_zm_x2_y], [6_z2_x2_y], [\bar 3_zm_y], [3_z2_y], [m_x^{\star}2_ym_z^{\star}], [2_x^{\star}2_y2_z^{\star}], [2_y/m_y^{\star}] 12 4 6 6
[\bar 1 ] [E_{1g}] [6_z/m_zm_xm_y ] [6_z/m_z], [\bar 3_z], [2_z^{\star}/m_z^{\star}], [2_x^{\star}/m_x^{\star}(3)], [2_y^{\star}/m_y^{\star}(3) ] 12 12 0 12
1 Reducible [6_z/m_zm_xm_y ] [\bar 6_z], [6_z], [\bar 3_z ], [3_z], [m_z^{\star}], [m_x^{\star}(3)], [m_y^{\star}(3) ], [2_z^{\star}], [2_x^{\star}(3)], [2_y^{\star}(3)], [\bar 1^{\star}] 24 24 24 12
[{\bf 23}] [3_p] [(3_q], [3_r], [3_s)] T [3_p] 23 4 1 4 4
[2_x2_y2_z] E 23 23 3 3 0 3
[2_z] [(2_x], [2_y)] T [2_x2_y2_z] [23], [2_x^{\star}2_y^{\star}2_z ] 6 2 6 6
1 T [23 ] [3_p(4)], [2_z^{\star}(3)] 12 12 12 12
[{\bi m}{\bar {\bf 3}} ] 23 [A_u ] [m\bar3] [m^{\star}\bar3^{\star}] 2 2 0 1
[\bar 3_p] [(\bar 3_q], [\bar3_r], [\bar 3_s) ] [T_g] [\bar3_p] [m\bar3] 4 1 0 4
[3_p] [(3_q], [3_r], [3_s)] [T_u] [\bar3_p] [m\bar3, 23 ] 8 2 8 4
[m_xm_ym_z] [E_g ] [m\bar3 ] [m\bar3] 3 3 0 3
[m_xm_y2_z ] [(2_xm_ym_z], [m_x2_ym_z)] [T_u ] [m_xm_ym_z] [m\bar3, m_xm_ym_z^{\star}] 6 2 6 3
[2_x2_y2_z] [E_u ] [m\bar3] [m\bar3], [23], [m_x^{\star}m_y^{\star}m_z^{\star} ] 6 6 0 3
[2_z/m_z] [(2_x/m_x], [2_y/m_y)] [T_g] [m_xm_ym_z] [m\bar3], [m_x^{\star}m_y^{\star}m_z ] 6 2 0 6
[m_z] [(m_x], [m_y)] [T_u ] [m_xm_ym_z ] [m\bar3], [2_x^{\star}m_y^{\star}m_z ], [m_x^{\star}2_y^{\star}m_z], [2_z^{\star}/m_z] 12 4 12 6
[2_z] [(2_x], [2_y)] Reducible [m_xm_ym_z] [m\bar3], [23], [m_x^{\star}m_y^{\star}2_z ], [2_x^{\star}2_y^{\star}2_z], [2_z/m_z^{\star}] 12 4 6 6
[\bar 1] [T_g ] [m\bar3] [\bar3_p(4)], [2_z^{\star}/m_z^{\star}(3) ] 12 12 0 12
1 [T_u ] [m\bar3] [\bar3_p(4)], [3_p(4)], [m_z^{\star}(3)], [2_z^{\star}(3)], [\bar1^{\star}] 24 24 24 12
[{\bf 432}] 23 [A_2] 432 [4^{\star}32^{\star}] 2 2 0 1
[3_p2_{x\bar{y}}] [(3_q2_{x\bar{y}} ], [ 3_r2_{xy}], [3_s2_{xy})] [T_2] [3_p2_{x\bar{y}} ] 432 4 1 0 4
[3_p] [(3_q], [3_r], [3_s)] [T_1] [3_p2_{x\bar{y}} ] [23], [3_p2_{x\bar{y}}^{\star} ] 8 2 8 4
[4_z2_x2_{xy}] [(4_x2_y2_{yz}], [4_y2_z2_{xz})] E [4_z2_x2_{xy}] 432 3 1 0 3
[4_z] [(4_x], [4_y)] [T_1] [4_z2_x2_{xy}] [432], [4_z2_x^{\star}2_{xy}^{\star} ] 6 2 6 3
[2_x2_y2_z] E 432 [23], [4_z^{\star}2_x2_{xy}^{\star} ] 6 6 0 6
[2_{x\bar{y}}2_{xy}2_z ] [(2_{y\bar{z}}2_{yz}2_x ], [2_{z\bar{x}}2_{zx}2_y)] [T_2] [4_z2_x2_{xy}] [432], [4_z^{\star}2_x^{\star}2_{xy} ] 6 2 0 6
[2_z] [(2_x], [2_y)] Reducible [4_z2_x2_{xy}] 23, [4_y2_z2_{xy}], [4_z^{\star} ], [2_{x\bar{y}}^{\star}2_{xy}^{\star}2_z], [2_x^{\star}2_y^{\star}2_z ] 12 4 6 12
[2_{xy}] [(2_{yz}], [2_{zx} ], [2_{x\bar{y}}], [2_{y\bar{z}}], [2_{z\bar{x}})] [T_1], [T_2 ] [2_{x\bar{y}}2_{xy}2_z ] [432], [3_r2_{xy}], [3_s2_{xy} ], [4_z2_x2_{xy}], [2_{x\bar{y}}2_{xy}^{\star}2_z^{\star}] 12 2 12 12
1 [T_1], [T_2 ] 432 [3_p(4) ], [4_z(3)], [2_z^{\star}(3) ], [2_{xy}^{\star}(6)] 24 24 24 24
[{\bar {\bf 4}}{\bf 3}{\bi m}] 23 [A_2 ] [\bar43m] [\bar4^{\star}3m^{\star} ] 2 2 0 1
[3_pm_{x\bar{y}}] [(3_qm_{x\bar{y}} ], [3_rm_{xy}], [3_sm_{xy})] [T_2] [3_pm_{x\bar{y}} ] [\bar43m ] 4 1 4 4
[3_p] [(3_q], [3_r], [3_s)] [T_1 ] [3_pm_{x\bar{y}} ] [\bar43m], [23], [3_pm_{x\bar{y}}^{\star} ] 8 2 4 4
[\bar4_z2_xm_{xy}] [(\bar4_x2_ym_{yz} ], [\bar4_y2_zm_{zx})] E [\bar4_z2_xm_{x\bar{y}}] [\bar43m] 3 1 0 3
[\bar4_z] [(\bar4_x, \bar4_y)] [T_1 ] [\bar4_z2_xm_{x\bar{y}}] [\bar43m], [\bar4_z2_x^{\star}m_{xy}^{\star} ] 6 2 0 3
[m_{x\bar{y}}m_{xy}2_z] [(m_{y\bar{z}}m_{yz}2_x ], [m_{z\bar{x}}m_{zx}2_y)] [T_2 ] [\bar4_z2_xm_{x\bar{y}}] [\bar43m], [\bar4_z^{\star}2_x^{\star}m_{xy} ] 6 2 6 6
[2_x2_y2_z] E [\bar43m ] [23, \bar4_z^{\star}2_xm_{xy}^{\star} ] 6 6 0 6
[m_{xy}] [(m_{yz}], [m_{zx} ], [m_{x\bar{y}}], [m_{y\bar{z}}], [m_{z\bar{x}})] [T_1, T_2] [m_{x\bar{y}}m_{xy}2_z] [\bar43m], [3_rm_{xy}], [3_sm_{xy}], [\bar4_z2_xm_{xy}], [m_{x\bar{y}}^{\star}m_{xy}2_z^{\star} ] 12 2 12 12
[2_z] [(2_x], [2_y)] Reducible [\bar4_z2_xm_{xy} ] 23, [\bar4_z^{\star}], [4_z^{\star} ], [m_{x\bar{y}}^{\star}m_{xy}^{\star}2_z], [2_x^{\star}2_y^{\star}2_z ] 12 4 6 12
1 [T_1], [T_2] [\bar43m ] [3_p(4) ], [\bar4_z(3)], [m_{xy}^{\star}(6)], [2_z^{\star}(3)] 24 24 24 24
[{\bi m}{\bar {\bf 3}}{\bi m} ] [\bar43m] [A_{2u}] [m\bar3m] [m^{\star}\bar3^{\star}m] 2 2 0 1
432 [A_{1u}] [m\bar3m] [m^{\star}\bar3^{\star}m^{\star}] 2 2 0 1
[m\bar3 ] [A_{2g}] [m\bar3m] [m\bar3m^{\star}] 2 2 0 1
23 Reducible [m\bar3m] [\bar4^{\star}3m^{\star}], [4^{\star}32^{\star} ], [m_z^{\star}\bar3_p ] 4 4 0 1
[\bar 3_pm_{x\bar{y}}] [(\bar 3_qm_{x\bar{y}} ], [\bar3_rm_{xy}], [\bar 3_sm_{xy})] [T_{2g}] [\bar3_pm_{x\bar{y}}] [m\bar3m] 4 1 0 4
[3_pm_{x\bar{y}}] [(3_qm_{x\bar{y}} ], [3_rm_{xy}], [3_sm_{xy})] [T_{1u}] [\bar3_pm_{x\bar{y}} ] [m\bar3m ], [\bar43m], [\bar3_p^{\star}m_{x\bar{y}}] 8 2 8 4
[3_p2_{x\bar{y}}] [(3_q2_{x\bar{y}} ], [3_r2_{xy}], [3_s2_{xy})] [T_{2u}] [\bar3_pm_{x\bar{y}} ] [m\bar3m], [432], [\bar3_p^{\star}m_{x\bar{y}} ] 8 2 0 4
[\bar 3_p] [(\bar 3_q], [\bar3_r], [\bar 3_s)] [T_{1g}] [\bar3_pm_{x\bar{y}}] [m\bar3m], [m\bar3], [\bar3_pm_{x\bar{y}}^{\star} ] 8 2 0 4
[3_p] [(3_q], [3_r], [3_s)] Reducible [\bar3_pm_{x\bar{y}}] [\bar43m], [432], [m\bar3 ], [23], [3_pm_{x\bar{y}}^{\star}], [3_p2_{x\bar{y}}^{\star} ], [\bar3_p^{\star}] 16 4 8 4
[4_z/m_zm_xm_{xy}] [(4_x/m_xm_ym_{yz} ], [4_y/m_ym_zm_{zx})] [E_g ] [4_z/m_zm_xm_{xy}] [m\bar3m] 3 1 0 3
[\bar4_z2_xm_{xy}] [(\bar4_x2_ym_{yz} ], [\bar4_y2_zm_{zx})] [E_u ] [4_z/m_zm_xm_{xy}] [m\bar3m], [\bar43m], [4_z^{\star}/m_z^{\star}m_x^{\star}m_{xy}] 6 2 0 3
[\bar4_zm_x2_{xy}] [(\bar4_xm_y2_{yz} ], [\bar4_ym_z2_{zx})] [T_{2u} ] [4_z/m_zm_xm_{xy}] [m\bar3m], [4_z^{\star}/m_z^{\star}m_xm_{xy}^{\star} ] 6 2 0 3
[4_zm_xm_{xy}] [(4_xm_ym_{yz}], [4_ym_zm_{zx})] [T_{1u} ] [4_z/m_zm_xm_{xy}] [m\bar3m], [4_z/m_z^{\star}m_xm_{xy} ] 6 2 6 3
[4_z2_x2_{xy}] [(4_x2_y2_{yz}], [4_y2_z2_{zx})] [E_u] [4_z/m_zm_xm_{xy} ] [m\bar3m], [432], [4_z/m_z^{\star}m_x^{\star}m_{xy}^{\star} ] 6 2 0 3
[4_z/m_z] [(4_x/m_x], [4_y/m_y)] [T_{1g} ] [4_z/m_zm_xm_{xy}] [m\bar3m], [4_z/m_zm_x^{\star}m_{xy}^{\star} ] 6 2 0 3
[\bar4_z] [(\bar4_x], [\bar4_y)] Reducible [4_z/m_zm_xm_{xy}] [m\bar3m], [\bar43m], [\bar4_z2_x^{\star}m_{xy}^{\star}], [\bar4_zm_x^{\star}2_{xy}^{\star} ], [4_z^{\star}/m_z^{\star}] 12 4 0 3
[4_z] [(4_x ], [4_y)] Reducible [4_z/m_zm_xm_{xy}] [m\bar3m], [432], [4_zm_x^{\star}m_{xy}^{\star} ], [4_z2_x^{\star}2_{xy}^{\star}], [4_z/m_z^{\star}] 12 4 6 3
[m_xm_ym_z] [E_g] [m\bar3m ] [m\bar3], [4_z^{\star}/m_zm_xm_{xy}^{\star} ] 6 6 0 6
[m_{x\bar{y}}m_{xy}m_z] [(m_{y\bar{z}}m_{yz}m_x ], [m_{z\bar{x}}m_{zx}m_y)] [T_{2g} ] [4_z/m_zm_xm_{xy}] [m\bar3m ], [4_z^{\star}/m_zm_xm_{xy}^{\star} ] 6 2 0 6
[m_xm_y2_z] [(2_xm_ym_z], [m_x2_ym_z)] Reducible [4_z/m_zm_xm_{xy}] [m\bar3], [4_y/m_ym_zm_{zx}], [\bar4_z^{\star}m_x2_{xy}^{\star}], [4_z^{\star}m_xm_{xy}^{\star}], [ m_xm_ym_z^{\star}] 12 4 6 6
[m_{x\bar{y}}m_{xy}2_z] [(m_{y\bar{z}}m_{yz}2_x ], [m_{z\bar{x}}m_{zx}2_y)] Reducible [4_z/m_zm_xm_{xy}] [m\bar3m], [\bar43m], [\bar4_z^{\star}2_x^{\star}m_{xy}], [4_z^{\star}m_x^{\star}m_{xy}], [m_{x\bar{y}}m_{xy}m_z^{\star}] 12 4 6 6
[m_{x\bar{y}}2_{xy}m_z] [(m_{y\bar{z}}2_{yz}m_x ], [m_{z\bar{x}}2_{zx}m_y], [ 2_{x\bar{y}}m_{xy}m_z], [2_{y\bar{z}}m_{yz}m_x], [2_{z\bar{x}}m_{zx}m_y)] [T_{1u}], [T_{2u}] [m_{x\bar{y}}m_{xy}m_z ] [m\bar3m(m_{zx})], [m\bar3m(2_{zx}) ], [4_z/m_zm_xm_{xy}], [ m_{x\bar{y}}m_{xy}^{\star}m_z] 12 2 12 6
[2_x2_y2_z] [E_u] [m\bar3m ] [m\bar3], [23], [\bar4_z^{\star}2_xm_{xy}^{\star} ], [4_z^{\star}2_x2^{\star}_{xy}], [m_x^{\star}m_y^{\star}m_z^{\star} ] 12 12 0 6
[2_{x\bar{y}}2_{xy}2_z] [(2_{y\bar{z}}2_{yz}2_x ], [2_{z\bar{x}}2_{zx}2_y)] Reducible [4_z/m_zm_xm_{xy}] [m\bar3m], [432], [\bar4_zm_x^{\star}2_{xy} ], [4^{\star}_z2^{\star}_x2_{xy}], [m_{x\bar{y}}^{\star}m_{xy}^{\star}m_z^{\star} ] 12 4 0 6
[2_z/m_z] [(2_x/m_x, 2_y/m_y)] Reducible [4_z/m_zm_xm_{x\bar{y}}] [m\bar3], [ 4_y/m_ym_zm_{zx}], [4_z^{\star}/m_z], [m_x^{\star}m_y^{\star}m_z], [m_{x\bar{y}}^{\star}m_{xy}^{\star}m_z ] 12 4 0 12
[2_{xy}/m_{xy}] [(2_{yz}/m_{yz} ], [2_{zx}/m_{zx}], [2_{x\bar{y}}/m_{x\bar{y}}], [2_{y\bar{z}}/m_{y\bar{z}} ], [2_{z\bar{x}}/m_{z\bar{x}})] [T_{1g}], [T_{2g}] [m_{x\bar{y}}m_{xy}m_z] [m\bar3m], [\bar3_rm_{xy} (2)], [4_z/m_zm_xm_{xy}], [m_{x\bar{y}}^{\star}m_{xy}m_z^{\star}] 12 2 0 12
[m_z] [(m_x], [m_y)] [T_{1u}], [T_{2u} ] [4_z/m_zm_xm_{x\bar{y}} ] [m\bar3], [\bar4_xm_z2_{yz} ], [4_ym_zm_{zx}], [4_z/m_z], [2_x^{\star}m_y^{\star}m_z (2) ], [m_{x\bar{y}}^{\star}2_{xy}^{\star}m_z(2)], [2_z^{\star}/m_z ] 24 8 24 12
[m_{xy}] [(m_{yz} ], [m_{zx}], [m_{x\bar{y}}], [m_{y\bar{z}}], [m_{z\bar{x}})] [T_{1u}] [m_{x\bar{y}}m_{xy}m_z ] [m\bar3m], [\bar43m ], [\bar4_z2_xm_{xy}], [4_zm_xm_{xy}], [\bar3_rm_{xy} ], [\bar3_sm_{xy}], [3_rm_{xy}], [3_sm_{xy}], [m_{x\bar{y}}^{\star}m_{xy}2_z^{\star} ], [2_{xy}^{\star}/m_{xy}] 24 4 24 12
[2_z] [(2_x], [2_y)] Reducible [4_z/m_zm_xm_{x\bar{y}} ] [m\bar3], [23], [\bar4_y2_zm_{zx}], [4_y2_z2_{zx}], [\bar4_z^{\star}], [4_z^{\star}], [m_x^{\star}m_y^{\star}2_z], [m_{x\bar{y}}^{\star}m_{xy}^{\star}2_z ], [2_x^{\star}2_y^{\star}2_z ], [2_{x\bar{y}}^{\star}2_{xy}^{\star}2_z ], [2_z/m_z^{\star}] 24 8 6 12
[2_{xy}] [(2_{yz} ], [ 2_{zx}], [2_{x\bar{y}}], [2_{y\bar{z}}], [2_{z\bar{x}})] [T_{2u}] [m_{x\bar{y}}m_{xy}m_z ] [m\bar3m], [432 ], [\bar3_rm_{xy}], [\bar3_sm_{xy}], [3_r2_{xy}], [3_s2_{xy}], [\bar4_zm_x2_{xy}], [4_z2_x2_{xy}], [m_{x\bar{y}}^{\star}2_{xy}m_z^{\star} ], [2_{x\bar{y}}^{\star}2_{xy}2_z^{\star}], [2_{xy}/m_{xy}^{\star} ] 24 4 12 12
[\bar 1] [T_{1g}], [T_{2g} ] [m\bar3m ] [\bar3_p(4)], [4_z/m_z(3)], [2_z^{\star}/m_z^{\star}(3)], [2_{xy}^{\star}/m_{xy}^{\star}(6) ] 24 24 0 24
1 [T_{1u}], [T_{2u} ] [m\bar3m ] [\bar3_p(4)], [\bar4_z(3)], [4_z(3)], [m_z^{\star}(3)], [m_{xy}^{\star}(6) ], [2_z^{\star}(3)], [2_{xy}^{\star}(6)], [ \bar1^{\star} ] 48 48 48 24
[u =x], y, z, [xy], [yz], [zx], [x\bar{y}], [y\bar{z}], [z\bar{x}], [x{^\prime}], [x{^\prime}{^\prime}], [y{^\prime} ], [y{^\prime}{^\prime}].