Character table for point group S4

S4 E S4 C2 (S4)3
linear functions,
rotations
quadratic
functions
cubic
functions
A +1 +1 +1 +1 Rz x2+y2, z2 xyz, z(x2-y2)
B +1 -1 +1 -1 z x2-y2, xy z3, z(x2+y2)
E +1
+1
+i
-i
-1
-1
-i
+i
x+iy; Rx+iRy
x-iy; Rx-iRy
(xz, yz) (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) no


Reduction formula for point group S4

Type of representation

Information for point groups with complex irreducible representations

general 3N vib

E S4 C2 (S4)3




Multipoles

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

First nonvanishing multipole: quadrupole

Literature



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