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## Point Group Tables of C2v(mm2)

 C2v(mm2) # 1 2z my mx functions A1 Γ1 1 1 1 1 z,x2,y2,z2 A2 Γ3 1 1 -1 -1 xy,Jz B1 Γ2 1 -1 1 -1 x,xz,Jy B2 Γ4 1 -1 -1 1 y,yz,Jx

 Subgroup Order Index C2v(mm2) 4 1 C2(2) 2 2 Cs(m) 2 2 C1(1) 1 4

[ Subduction tables ]

 C2v(mm2) A1 A2 B1 B2 A1 A1 A2 B1 B2 A2 · A1 B2 B1 B1 · · A1 A2 B2 · · · A1

[ Note: the table is symmetric ]

 C2v(mm2) A1 A2 B1 B2 [A1 x A1] 1 · · · [A2 x A2] 1 · · · [B1 x B1] 1 · · · [B2 x B2] 1 · · ·

 C2v(mm2) A1 A2 B1 B2 {A1 x A1} · · · · {A2 x A2} · · · · {B1 x B1} · · · · {B2 x B2} · · · ·

 C2v(mm2) A1 A2 B1 B2 V 1 · 1 1 [V2] 3 1 1 1 [V3] 3 1 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 5 3 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 A1 A2 B1 B2 A1 x · x x A2 · x x x B1 x x x · B2 x x · x

[ Note: x means allowed ]

 Raman A1 A2 B1 B2 A1 x x x x A2 x x x x B1 x x x x B2 x x x x

[ Note: x means allowed ]

 Irreps Dimensions Irreps of the point group L 2L+1 A1 A2 B1 B2 0 1 1 · · · 1 3 1 · 1 1 2 5 2 1 1 1 3 7 2 1 2 2 4 9 3 2 2 2 5 11 3 2 3 3 6 13 4 3 3 3 7 15 4 3 4 4 8 17 5 4 4 4 9 19 5 4 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.