Character table for point group C5

Character table for point group C₅

=exp(2

i/5)

C₅	E	C₅	(C₅)²	(C₅)³	(C₅)⁴	linear functions, rotations	quadratic functions	cubic functions
A	+1	+1	+1	+1	+1	z, R_z	x²+y², z²	z³, z(x²+y²)
E₁	+1 +1	+ +^*	+² +^2*	+^2* +²	+^* +	x+iy, R_x+iR_y x-iy, R_x-iR_y	(yz, xz)	(xz², yz²) [x(x²+y²), y(x²+y²)]
E₂	+1 +1	+² +^2*	+^* +	+ +^*	+^2* +²	-	(x²-y², xy)	[xyz, z(x²-y²)] [y(3x²-y²), x(x²-3y²)]

Information for point groups with fivefold rotational axis

Additional information

Number of symmetry elements	h = 5
Number of irreducible representations	n = 5
Number of real irreducible representations	n = 3
Abelian group	yes
Optical Isomerism (Chirality)	yes
Polar	yes

Reduction formula for point group C₅

Multipoles

dipole (p)	A+E₁
quadrupole (d)	A+E₁+E₂
octopole (f)	A+E₁+2E₂
hexadecapole (g)	A+2E₁+2E₂
32-pole (h)	3A+2E₁+2E₂
64-pole (i)	3A+3E₁+2E₂
128-pole (j)	3A+3E₁+3E₂
256-pole(k)	3A+3E₁+4E₂
512-pole (l)	3A+4E₁+4E₂

First nonvanishing multipole: dipole

Literature

A. Gelessus, W. Thiel and W. Weber, J. Chem. Educ. 72, 505 (1995)
Multipoles and Symmetry

Character tables for chemically important point groups

Computational Laboratory for Analysis, Modeling and Visualization

Constructor University Bremen

Last update November, 13^th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement