d5d - Point Group Symmetry Character Tables - Chemistry Online Education

d5d - Point Group Symmetry Character Tables

Nonaxial
C₁
C_s
C_i

C_n
C₂
C₃
C₄
C₅
C₆

C_nv
C_2v
C_3v
C_4v
C_5v
C_6v

C_nh
C_2h
C_3h
C_4h
C_5h
C_6h

D_n
D₂
D₃
D₄
D₅
D₆

D_nh
D_2h
D_3h
D_4h
D_5h
D_6h

D_nd
D_2d
D_3d
D_4d
D_5d
D_6d

S_n
S₄
S₆
S₈
S₁₀

Higher
T_d
O_h
I_h

Linear
C_∞v
D_∞h

D_5d Point Group

not Abelian, 8(12) irreducible representations

Subgroups of D_5d point group: C_s, C_i, C₂, C₅, D₅, C_5v, S₁₀

Character table for D_5d point group

	E	2C₅	2(C₅)²	5C'₂	i	2(S₁₀)³	2S₁₀	5σ_d	linear, rotations	quadratic
A_1g	1	1	1	1	1	1	1	1		x²+y², z²
A_2g	1	1	1	-1	1	1	1	-1	R_z
E_1g	2	2cos(2π/5)	2cos(4π/5)	0	2	2cos(2π/5)	2cos(4π/5)	0	(R_x, R_y)	(xz, yz)
E_2g	2	2cos(4π/5)	2cos(2π/5)	0	2	2cos(4π/5)	2cos(2π/5)	0		(x²-y², xy)
A_1u	1	1	1	1	-1	-1	-1	-1
A_2u	1	1	1	-1	-1	-1	-1	1	z
E_1u	2	2cos(2π/5)	2cos(4π/5)	0	-2	-2cos(2π/5)	-2cos(4π/5)	0	(x, y)
E_2u	2	2cos(4π/5)	2cos(2π/5)	0	-2	-2cos(4π/5)	-2cos(2π/5)	0

Product table for D_5d point group

	A_1g	A_2g	E_1g	E_2g	A_1u	A_2u	E_1u	E_2u
A_1g	A_1g	A_2g	E_1g	E_2g	A_1u	A_2u	E_1u	E_2u
A_2g	A_2g	A_1g	E_1g	E_2g	A_2u	A_1u	E_1u	E_2u
E_1g	E_1g	E_1g	A_1g+A_2g+E_2g	E_1g+E_2g	E_1u	E_1u	A_1u+A_2u+E_2u	E_1u+E_2u
E_2g	E_2g	E_2g	E_1g+E_2g	A_1g+A_2g+E_2g	E_2u	E_2u	E_1u+E_2u	A_1u+A_2u+E_2u
A_1u	A_1u	A_2u	E_1u	A_2u	A_1g	A_2g	E_1g	E_2g
A_2u	A_2u	A_1u	E_1u	E_2u	A_2g	A_1g	E_1g	E_2g
E_1u	E_1u	E_1u	A_1u+A_2u+E_2u	E_1u+E_2u	E_1g	E_1g	A_1g+A_2g+E_2g	E_1g+E_2g
E_2u	E_2u	E_2u	E_1u+E_2u	A_1u+A_2u+E_2u	E_2g	E_2g	E_1g+E_2g	A_1g+A_2g+E_2g

Printable D_5d point group
Printable character table for D_5d point group
Printable product table for D_5d point group

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