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## Point Group Tables of D2(222)

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 D2(222) # 1 2z 2y 2x functions A Γ1 1 1 1 1 x2,y2,z2 B1 Γ3 1 1 -1 -1 z,xy,Jz B2 Γ2 1 -1 1 -1 y,xz,Jy B3 Γ4 1 -1 -1 1 x,yz,Jx

 Subgroup Order Index D2(222) 4 1 C2(2) 2 2 C1(1) 1 4

[ Subduction tables ]

 D2(222) A B1 B2 B3 A A B1 B2 B3 B1 · A B3 B2 B2 · · A B1 B3 · · · A

[ Note: the table is symmetric ]

 D2(222) A B1 B2 B3 [A x A] 1 · · · [B1 x B1] 1 · · · [B2 x B2] 1 · · · [B3 x B3] 1 · · ·

 D2(222) A B1 B2 B3 {A x A} · · · · {B1 x B1} · · · · {B2 x B2} · · · · {B3 x B3} · · · ·

 D2(222) A B1 B2 B3 V · 1 1 1 [V2] 3 1 1 1 [V3] 1 3 3 3 [V4] 6 3 3 3 A · 1 1 1 [A2] 3 1 1 1 [A3] 1 3 3 3 [A4] 6 3 3 3 [V2]xV 3 5 5 5 [[V2]2] 9 4 4 4 {V2} · 1 1 1 {A2} · 1 1 1 {[V2]2} 3 4 4 4

V ≡ the vector representation
A ≡ the axial representation

 IR A B1 B2 B3 A · x x x B1 x · x x B2 x x · x B3 x x x ·

[ Note: x means allowed ]

 Raman A B1 B2 B3 A x x x x B1 x x x x B2 x x x x B3 x x x x

[ Note: x means allowed ]

 Irreps Dimensions Irreps of the point group L 2L+1 A B1 B2 B3 0 1 1 · · · 1 3 · 1 1 1 2 5 2 1 1 1 3 7 1 2 2 2 4 9 3 2 2 2 5 11 2 3 3 3 6 13 4 3 3 3 7 15 3 4 4 4 8 17 5 4 4 4 9 19 4 5 5 5 10 21 6 5 5 5

* George F. Koster, John O. Dimmock, Robert G. Wheeler, Hermann Statz (1963). Properties of the thirty-two point groups. Published by the M.I.T. press, Cambridge, Massachusetts.
* Simon L. Altmann and Peter Herzig (1994). Point-Group Theory Tables. Oxford Science Publications.

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