Character table for point group C3h

=exp(2i/3)
C3h E C3(z) (C3)2 h S3 (S3)5
linear functions,
rotations
quadratic
functions
cubic
functions
A' +1 +1 +1 +1 +1 +1 Rz x2+y2, z2 y(3x2-y2), x(x2-3y2)
E' +1
+1
+
+*
+*
+
+1
+1
+
+*
+*
+
x+iy
x-iy
(x2-y2, xy) (xz2, yz2) [x(x2+y2), y(x2+y2)]
A'' +1 +1 +1 -1 -1 -1 z - z3, z(x2+y2)
E'' +1
+1
+
+*
+*
+
-1
-1
-
-*
-*
-
Rx+iRy
Rx-iRy
(xz, yz) [xyz, z(x2-y2)]


Additional information

Number of symmetry elements h = 6
Number of irreducible representations n = 6
Number of real irreducible representations n = 4
Abelian group yes
Number of subgroups2
Subgroups Cs , C3
Optical Isomerism (Chirality) no


Reduction formula for point group C3h

Type of representation

Information for point groups with complex irreducible representations

general 3N vib

E C3(z) (C3)2 h S3 (S3)5




Multipoles

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

First nonvanishing multipole: quadrupole

Literature



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