Character table for point group C5h

=exp(2i/5)
C5h E C5 (C5)2 (C5)3 (C5)4 h S5 (S5)7 (S5)3 (S5)9
linear functions,
rotations
quadratic
functions
cubic
functions
A' +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 Rz x2+y2, z2 -
E'1 +1
+1
+
+*
+2
+2*
+2*
+2
+*
+
+1
+1
+
+*
+2
+2*
+2*
+2
+*
+
x+iy
x-iy
- (xz2, yz2) [x(x2+y2), y(x2+y2)]
E'2 +1
+1
+2
+2*
+*
+
+
+*
+2*
+2
+1
+1
+2
+2*
+*
+
+
+*
+2*
+2
- (x2-y2, xy) [y(3x2-y2), x(x2-3y2)]
A'' +1 +1 +1 +1 +1 -1 -1 -1 -1 -1 z - z3, z(x2+y2)
E''1 +1
+1
+
+*
+2
+2*
+2*
+2
+*
+
-1
-1
-
-*
-2
-2*
-2*
-2
-*
-
Rx+iRy
Rx-iRy
(xz, yz) -
E''2 +1
+1
+2
+2*
+*
+
+
+*
+2*
+2
-1
-1
-2
-2*
-*
-
-
-*
-2*
-2
- - [xyz, z(x2-y2)]

Information for point groups with fivefold rotational axis


Additional information

Number of symmetry elements h = 10
Number of irreducible representations n = 10
Number of real irreducible representations n = 6
Abelian group yes
Number of subgroups2
Subgroups Cs , C5
Optical Isomerism (Chirality) no


Reduction formula for point group C5h

Type of representation

Information for point groups with complex irreducible representations

general 3N vib

E C5 (C5)2 (C5)3 (C5)4 h S5 (S5)7 (S5)3 (S5)9




Multipoles

dipole (p) E'1+A''
quadrupole (d) A'+E'2+E''1
octopole (f) E'1+E'2+A''+E''2
hexadecapole (g) A'+E'1+E'2+E''1+E''2
32-pole (h) 2A'+E'1+E'2+A''+E''1+E''2
64-pole (i) A'+2E'1+E'2+2A''+E''1+E''2
128-pole (j) 2A'+E'1+2E'2+A''+2E''1+E''2
256-pole(k) A'+2E'1+2E'2+2A''+E''1+2E''2
512-pole (l) 2A'+2E'1+2E'2+A''+2E''1+2E''2

First nonvanishing multipole: quadrupole

Literature



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