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## Point Group Tables of C3(3)

 C3(3) # 1 3+ 3- functions A Γ1 1 1 1 z,x2+y2,z2,Jz 1E2E Γ3Γ2 11 w2w ww2 (x,y),(xz,yz),(x2-y2,xy),(Jx,Jy)

w = exp(2iπ/3)

 Subgroup Order Index C3(3) 3 1 C1(1) 1 3

[ Subduction tables ]

 C3(3) A 1E 2E A A 1E 2E 1E · 2E A 2E · · 1E

[ Note: the table is symmetric ]

 C3(3) A 1E 2E [A x A] 1 · · [1E x 1E] · · 1 [2E x 2E] · 1 ·

 C3(3) A 1E 2E {A x A} · · · {1E x 1E} · · · {2E x 2E} · · ·

 C3(3) A 1E 2E V 1 1 1 [V2] 2 2 2 [V3] 4 3 3 [V4] 5 5 5 A 1 1 1 [A2] 2 2 2 [A3] 4 3 3 [A4] 5 5 5 [V2]xV 6 6 6 [[V2]2] 7 7 7 {V2} 1 1 1 {A2} 1 1 1 {[V2]2} 5 5 5

V ≡ the vector representation
A ≡ the axial representation

 IR A 1E 2E A x x x 1E x x x 2E x x x

[ Note: x means allowed ]

 Raman A 1E 2E A x x x 1E x x x 2E x x x

[ Note: x means allowed ]

 Irreps Dimensions Irreps of the point group L 2L+1 A 1E 2E 0 1 1 · · 1 3 1 1 1 2 5 1 2 2 3 7 3 2 2 4 9 3 3 3 5 11 3 4 4 6 13 5 4 4 7 15 5 5 5 8 17 5 6 6 9 19 7 6 6 10 21 7 7 7

* C. J. Bradley and A. P. Cracknell (1972) The Mathematical Theory of Symmetry in Solids Clarendon Press - Oxford
* Simon L. Altmann and Peter Herzig (1994). Point-Group Theory Tables. Oxford Science Publications.

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