Character table for point group C4

C4 E C4 C2 (C4)3
linear functions,
A +1 +1 +1 +1 z, Rz x2+y2, z2 z3, z(x2+y2)
B +1 -1 +1 -1 - x2-y2, xy xyz, z(x2-y2)
E +1
x+iy; Rx+iRy
x-iy; Rx-iRy
(yz, xz) (xz2, yz2) (xy2, x2y) (x3, y3)

Additional information

Number of symmetry elements h = 4
Number of irreducible representations n = 4
Number of real irreducible representations n = 3
Abelian group yes
Number of subgroups1
Subgroup C2
Optical Isomerism (Chirality) yes
Polar yes

Reduction formula for point group C4

Type of representation

Information for point groups with complex irreducible representations

general 3N vib

E C4 C2 (C4)3


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

First nonvanishing multipole: dipole


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

Last update Mai, 23rd 2018 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement