Character table for point group S10

=exp(2i/5)
S10 E C5 (C5)2 (C5)3 (C5)4 i (S10)7 (S10)9 S10 (S10)3
linear functions,
rotations
quadratic
functions
cubic
functions
Ag +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 Rz z2, x2+y2 -
E1g +1
+1
+
+*
+2
+2*
+2*
+2
+*
+
+1
+1
+
+*
+2
+2*
+2*
+2
+*
+
Rx+iRy
Rx-iRy
(xz, yz) -
E2g +1
+1
+2
+2*
+*
+
+
+*
+2*
+2
+1
+1
+2
+2*
+*
+
+
+*
+2*
+2
- (x2-y2, xy) -
Au +1 +1 +1 +1 +1 -1 -1 -1 -1 -1 z - z3, z(x2+y2)
E1u +1
+1
+
+*
+2
+2*
+2*
+2
+*
+
-1
-1
-
-*
-2
-2*
-2*
-2
-*
-
x+iy
x-iy
- (xz2, yz2) [x(x2+y2), y(x2+y2)]
E2u +1
+1
+2
+2*
+*
+
+
+*
+2*
+2
-1
-1
-2
-2*
-*
-
-
-*
-2*
-2
- - [xyz, z(x2-y2)] [y(3x2-y2), x(x2-3y2)]


Additional information

Number of symmetry elements h = 10
Number of irreducible representations n = 10
Number of real irreducible representations n = 6
Abelian group yes
Subgroups Ci , C5
Optical Isomerism (Chirality) no


Reduction formula for point group S10

Type of representation

Information for point groups with complex irreducible representations

general 3N vib

E C5 (C5)2 (C5)3 (C5)4 i (S10)7 (S10)9 S10 (S10)3




Multipoles

dipole (p) Au+E1u
quadrupole (d) Ag+E1g+E2g
octopole (f) Au+E1u+2E2u
hexadecapole (g) Ag+2E1g+2E2g
32-pole (h) 3Au+2E1u+2E2u
64-pole (i) 3Ag+3E1g+2E2g
128-pole (j) 3Au+3E1u+3E2u
256-pole(k) 3Ag+3E1g+4E2g
512-pole (l) 3Au+4E1u+4E2u

First nonvanishing multipole: quadrupole

Literature



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