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## Point Group Tables of C3v(3m)

 C3v(3m) # 1 3 m functions Mult. - 1 2 3 · A1 Γ1 1 1 1 z,x2+y2,z2 A2 Γ2 1 1 -1 Jz E Γ3 2 -1 0 (x,y),(xz,yz),(x2-y2,xy),(Jx,Jy)

 Subgroup Order Index C3v(3m) 6 1 C3(3) 3 2 Cs(m) 2 3 C1(1) 1 6

[ Subduction tables ]

 C3v(3m) A1 A2 E A1 A1 A2 E A2 · A1 E E · · A1+A2+E

[ Note: the table is symmetric ]

 C3v(3m) A1 A2 E [A1 x A1] 1 · · [A2 x A2] 1 · · [E x E] 1 · 1

 C3v(3m) A1 A2 E {A1 x A1} · · · {A2 x A2} · · · {E x E} · 1 ·

 C3v(3m) A1 A2 E V 1 · 1 [V2] 2 · 2 [V3] 3 1 3 [V4] 4 1 5 A · 1 1 [A2] 2 · 2 [A3] 1 3 3 [A4] 4 1 5 [V2]xV 4 2 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 2 1 2 4 9 2 1 3 5 11 2 1 4 6 13 3 2 4 7 15 3 2 5 8 17 3 2 6 9 19 4 3 6 10 21 4 3 7

* 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.