Character table for point group S12

=exp(2i/12)
S12 E S12 C6 S4 C3 (S12)5 C2 (S12)7 (C3)2 (S4)3 (C6)5 (S12)11
linear functions,
rotations
quadratic
functions
cubic
functions
A +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 Rz z2, x2+y2 -
B +1 -1 +1 -1 +1 -1 +1 -1 +1 -1 +1 -1 z - z3, z(x2+y2)
E1 +1
+1		 +
+*		+2
+2*		+i
-i		-2*
-2		-*
-		-1
-1		-
-*		 -2
-2*		 -i
+i		 +2*
+2		 +*
+		 x+iy
x-iy		 - (xz2, yz2) [x(x2+y2), y(x2+y2)]
E2 +1
+1		 +2
+2*		-2*
-2		-1
-1		-2
-2*		+2*
+2		+1
+1		+2
+2*		 -2*
-2		 -1
-1		 -2
-2*		 +2*
+2		 - (x2-y2, xy) -
E3 +1
+1		 +i
-i		-1
-1		-i
+i		+1
+1		+i
-i		-1
-1		-i
+i		 +1
+1		 +i
-i		 -1
-1		 -i
+i		 - - [x(x2-3y2), y(3x2-y2)]
E4 +1
+1		 -2*
-2		-2
-2*		+1
+1		-2*
-2		-2
-2*		+1
+1		-2*
-2		 -2
-2*		 +1
+1		 -2*
-2		 -2
-2*		 - - [xyz, z(x2-y2)]
E5 +1
+1		 -*
-		+2*
+2		+i
-i		-2
-2*		+
+*		-1
-1		+*
+		 -2*
-2		 -i
+i		 +2
+2*		 -
-*		 Rx-iRy
Rx+iRy		 (xz, yz) -


Additional information

Number of symmetry elements h = 12
Number of irreducible representations n = 12
Number of real irreducible representations n = 7
Abelian group yes
Number of subgroups4
Subgroups C2 , C3 , C6 , S4
Optical Isomerism (Chirality) no
Polar no


Reduction formula for point group S12

Type of representation

Information for point groups with complex irreducible representations

general 3N vib

E S12 C6 S4 C3 (S12)5 C2 (S12)7 (C3)2 (S4)3 (C6)5 (S12)11



Multipoles

dipole (p) B+E1
quadrupole (d) A+E2+E5
octopole (f) B+E1+E3+E4
hexadecapole (g) A+E2+E3+E4+E5
32-pole (h) B+E1+E2+E3+E4+E5
64-pole (i) A+2B+E1+E2+E3+E4+E5
128-pole (j) 2A+B+E1+E2+E3+E4+2E5
256-pole(k) A+2B+2E1+E2+E3+2E4+E5
512-pole (l) 2A+B+E1+2E2+2E3+E4+2E5

First nonvanishing multipole: quadrupole

Literature


Character tables for chemically important point groups Computational Laboratory for Analysis, Modeling and Visualization Constructor University Bremen
Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement