Character table for point group S6

=exp(2i/3)
S6 E C3(z) (C3)2 i (S6)5 S6
linear functions,
rotations
quadratic
functions
cubic
functions
Ag +1 +1 +1 +1 +1 +1 Rz x2+y2, z2 -
Eg +1
+1
+
+*
+*
+
+1
+1
+
+*
+*
+
Rx+iRy
Rx-iRy
(x2-y2, xy) (xz, yz) -
Au +1 +1 +1 -1 -1 -1 z - z3, y(3x2-y2), x(x2-3y2), z(x2+y2)
Eu +1
+1
+
+*
+*
+
-1
-1
-
-*
-*
-
x+iy
x-iy
- (xz2, yz2) [xyz, z(x2-y2)] [x(x2+y2), y(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
Subgroups Ci , C3
Optical Isomerism (Chirality) no


Reduction formula for point group S6

Type of representation

Information for point groups with complex irreducible representations

general 3N vib

E C3(z) (C3)2 i (S6)5 S6




Multipoles

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

First nonvanishing multipole: quadrupole

Literature



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