Character table for point group C3

=exp(2i/3)
C3 E C3 (C3)2
linear functions,
rotations
quadratic
functions
cubic
functions
A +1 +1 +1 z, Rz x2+y2, z2 z3, y(3x2-y2), x(x2-3y2), z(x2+y2)
E +1
+1
+
+*
+*
+
x+iy; Rx+iRy
x-iy; Rx-iRy
(x2-y2, xy) (yz, xz) (xz2, yz2) [xyz, z(x2-y2)] [x(x2+y2), y(x2+y2)]


Additional information

Number of symmetry elements h = 3
Number of irreducible representations n = 3
Number of real irreducible representations n = 2
Abelian group yes
Optical Isomerism (Chirality) yes


Reduction formula for point group C3

Type of representation

Information for point groups with complex irreducible representations

general 3N vib

E C3 (C3)2




Multipoles

dipole (p) A+E
quadrupole (d) A+2E
octopole (f) 3A+2E
hexadecapole (g) 3A+3E
32-pole (h) 3A+4E
64-pole (i) 5A+4E
128-pole (j) 5A+5E
256-pole(k) 5A+6E
512-pole (l) 7A+6E

First nonvanishing multipole: dipole

Literature



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