Character table for point group C4

C4 E C4 C2 (C4)3
linear functions,
rotations
quadratic
functions
cubic
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
+1
+i
-i
-1
-1
-i
+i
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
Subgroup C2
Optical Isomerism (Chirality) 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




Multipoles

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

Literature



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