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## Point Group Tables of D3(32)

 D3(32) # 1 3 21-10 functions Mult. - 1 2 3 · A1 Γ1 1 1 1 x2+y2,z2 A2 Γ2 1 1 -1 z,Jz E Γ3 2 -1 0 (x,y),(xz,yz),(x2-y2,xy),(Jx,Jy)

 Subgroup Order Index D3(32) 6 1 C3(3) 3 2 C2(2) 2 3 C1(1) 1 6

[ Subduction tables ]

 D3(32) A1 A2 E A1 A1 A2 E A2 · A1 E E · · A1+A2+E

[ Note: the table is symmetric ]

 D3(32) A1 A2 E [A1 x A1] 1 · · [A2 x A2] 1 · · [E x E] 1 · 1

 D3(32) A1 A2 E {A1 x A1} · · · {A2 x A2} · · · {E x E} · 1 ·

 D3(32) A1 A2 E V · 1 1 [V2] 2 · 2 [V3] 1 3 3 [V4] 4 1 5 A · 1 1 [A2] 2 · 2 [A3] 1 3 3 [A4] 4 1 5 [V2]xV 2 4 6 [[V2]2] 6 1 7 {V2} · 1 1 {A2} · 1 1 {[V2]2} 2 3 5

V ≡ the vector representation
A ≡ the axial representation

 IR A1 A2 E A1 · x x A2 x · x E x x x

[ Note: x means allowed ]

 Raman A1 A2 E A1 x · x A2 · x x E x x x

[ Note: x means allowed ]

 Irreps Dimensions Irreps of the point group L 2L+1 A1 A2 E 0 1 1 · · 1 3 · 1 1 2 5 1 · 2 3 7 1 2 2 4 9 2 1 3 5 11 1 2 4 6 13 3 2 4 7 15 2 3 5 8 17 3 2 6 9 19 3 4 6 10 21 4 3 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.