d5d - Point Group Symmetry Character Tables - Chemistry Online Education

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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

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