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Number of constants needed to specify the dipole and quadrupole in various point groups

Point Group dipole quadrupole
C∞v 1 1
C1 3 5
C2 1 3
C2h 0 3
C2v 1 2
C3 1 1
C3h 0 1
C3v 1 1
C4 1 1
C4h 0 1
C4v 1 1
C5 1 1
C5h 0 1
C5v 1 1
C6 1 1
C6h 0 1
C6v 1 1
C7v 1 1
Ci 0 5
Cs 2 3
D∞h 0 1
D2 0 2
D2d 0 1
D2h 0 2
D3 0 1
D3d 0 1
D3h 0 1
D4 0 1
D4d 0 1
D4h 0 1
D5d 0 1
D5h 0 1
D6h 0 1
D7h 0 1
Ih 0 0
Kh 0 0
Oh 0 0
S4 0 1
S6 0 1
T 0 0
Td 0 0
Th 0 0