Character table for point group C6v

C6v E 2C6 (z) 2C3 (z) C2 (z) 3v 3d
linear functions,
rotations
quadratic
functions
cubic
functions
A1 +1 +1 +1 +1 +1 +1 z x2+y2, z2 z3, z(x2+y2)
A2 +1 +1 +1 +1 -1 -1 Rz - -
B1 +1 -1 +1 -1 +1 -1 - - x(x2-3y2)
B2 +1 -1 +1 -1 -1 +1 - - y(3x2-y2)
E1 +2 +1 -1 -2 0 0 (x, y) (Rx, Ry) (xz, yz) (xz2, yz2) [x(x2+y2), y(x2+y2)]
E2 +2 -1 -1 +2 0 0 - (x2-y2, xy) [xyz, z(x2-y2)]


Additional information

Number of symmetry elements h = 12
Number of irreducible representations n = 6
Abelian group no
Number of subgroups8
Number of distinct subgroups6
Subgroups
(Number of different orientations)
Cs (2) , C2 , C3 , C6 , C2v , C3v (2)
Optical Isomerism (Chirality) no
Polar yes


Reduction formula for point group C6v

Type of representation

general 3N vib

E 2C6 (z) 2C3 (z) C2 (z) 3v 3d




Multipoles

dipole (p) A1+E1
quadrupole (d) A1+E1+E2
octopole (f) A1+B1+B2+E1+E2
hexadecapole (g) A1+B1+B2+E1+2E2
32-pole (h) A1+B1+B2+2E1+2E2
64-pole (i) 2A1+A2+B1+B2+2E1+2E2
128-pole (j) 2A1+A2+B1+B2+3E1+2E2
256-pole(k) 2A1+A2+B1+B2+3E1+3E2
512-pole (l) 2A1+A2+2B1+2B2+3E1+3E2

First nonvanishing multipole: dipole

Literature



Character tables for chemically important point groups Computational Laboratory for Analysis, Modeling and Visualization Constructor University Bremen

Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement