d6d - Point Group Symmetry Character Tables - Chemistry Online Education

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Linear
C_∞v
D_∞h

D_6d Point Group

not Abelian, 9(14) irreducible representations

Subgroups of D_6d point group: C_s, C₂, C₃, C₆, D₂, D₃, D₆, C_2v, C_3v, C_6v, S₄, S₁₂

Character table for D_6d point group

	E	2S₁₂	2C₆	2S₄	2C₃	2(S₁₂)⁵	C₂	6C'₂	6σ_d	linear, rotations	quadratic
A₁	1	1	1	1	1	1	1	1	1		x²+y², z²
A₂	1	1	1	1	1	1	1	-1	-1	R_z
B₁	1	-1	1	-1	1	-1	1	1	-1
B₂	1	-1	1	-1	1	-1	1	-1	1	z
E₁	2	(3)^1/2	1	0	-1	-(3)^1/2	-2	0	0	(x, y)
E₂	2	1	-1	-2	-1	1	2	0	0		(x²-y², xy)
E₃	2	0	-2	0	2	0	-2	0	0
E₄	2	-1	-1	2	-1	-1	2	0	0
E₅	2	-(3)^1/2	1	0	-1	(3)^1/2	-2	0	0	(R_x, R_y)	(xz, yz)

Product table for D_6d point group

Printable: character table for D_6d product table for D_6d D_6d point group