Character table for point group T

=exp(2i/3)
T E 4C3 4(C3)2 3C2
linear functions,
rotations
quadratic
functions
cubic
functions
A +1 +1 +1 +1 - x2+y2+z2 xyz
E +1
+1
+
+*
+*
+
+1
+1
- (x2-y2, 2z2-x2-y2) -
T +3 0 0 -1 (x, y, z) (Rx, Ry, Rz) (xy, xz, yz) (x3, y3, z3) (xy2, x2z, yz2) (xz2, x2y, y2z)


Additional information

Number of symmetry elements h = 12
Number of irreducible representations n = 4
Number of real irreducible representations n = 3
Abelian group no
Number of subgroups3
Subgroups C2 , C3 , D2
Optical Isomerism (Chirality) yes


Reduction formula for point group T

Type of representation

Information for point groups with complex irreducible representations

general 3N vib

E 4C3 4(C3)2 3C2




Examples

Neopentane (rotated)



Multipoles

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

First nonvanishing multipole: octopole

Literature



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