Character table for point group C6

=exp(2i/6)
C6 E C6 C3 C2 (C3)2 (C6)5
linear functions,
rotations
quadratic
functions
cubic
functions
A +1 +1 +1 +1 +1 +1 z, Rz x2+y2, z2 z3, z(x2+y2)
B +1 -1 +1 -1 +1 -1 - - y(3x2-y2), x(x2-3y2)
E1 +1
+1
+
+*
-*
-
-1
-1
-
-*
+*
+
x+iy; Rx+iRy
x-iy; Rx-iRy
(xz, yz) (xz2, yz2) [x(x2+y2), y(x2+y2)]
E2 +1
+1
-*
-
-
-*
+1
+1
-*
-
-
-*
- (x2-y2, xy) [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 C2 , C3
Optical Isomerism (Chirality) yes


Reduction formula for point group C6

Type of representation

Information for point groups with complex irreducible representations

general 3N vib

E C6 C3 C2 (C3)2 (C6)5




Multipoles

dipole (p) A+E1
quadrupole (d) A+E1+E2
octopole (f) A+2B+E1+E2
hexadecapole (g) A+2B+E1+2E2
32-pole (h) A+2B+2E1+2E2
64-pole (i) 3A+2B+2E1+2E2
128-pole (j) 3A+2B+3E1+2E2
256-pole(k) 3A+2B+3E1+3E2
512-pole (l) 3A+4B+3E1+3E2

First nonvanishing multipole: dipole

Literature



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