Character table for point group D2

D2 E C2 (z) C2 (y) C2 (x)
linear functions,
rotations
quadratic
functions
cubic
functions
A +1 +1 +1 +1 - x2, y2, z2 xyz
B1 +1 +1 -1 -1 z, Rz xy z3, y2z, x2z
B2 +1 -1 +1 -1 y, Ry xz yz2, x2y, y3
B3 +1 -1 -1 +1 x, Rx yz xz2, xy2, x3


Additional information

Number of symmetry elements h = 4
Number of irreducible representations n = 4
Abelian group yes
Number of subgroups3
Number of distinct subgroups1
Subgroup
(Number of different orientations)
C2 (3)
Optical Isomerism (Chirality) yes


Reduction formula for point group D2

Type of representation

general 3N vib

E C2 (z) C2 (y) C2 (x)




Multipoles

dipole (p) B1+B2+B3
quadrupole (d) 2A+B1+B2+B3
octopole (f) A+2B1+2B2+2B3
hexadecapole (g) 3A+2B1+2B2+2B3
32-pole (h) 2A+3B1+3B2+3B3
64-pole (i) 4A+3B1+3B2+3B3
128-pole (j) 3A+4B1+4B2+4B3
256-pole(k) 5A+4B1+4B2+4B3
512-pole (l) 4A+5B1+5B2+5B3

First nonvanishing multipole: quadrupole

Literature



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