d4d - Point Group Symmetry Character Tables - Chemistry Online Education

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Linear
C_∞v
D_∞h

D_4d Point Group

not Abelian, 7(10) irreducible representations

Subgroups of D_4d point group: C_s, C₂, C₄, D₂, D₄, C_2v, C_4v, S₈

Character table for D_4d point group

	E	2S₈	2C₄	2(S₈)³	C₂	4C'₂	4σ_d	linear, rotations	quadratic
A₁	1	1	1	1	1	1	1		x²+y², z²
A₂	1	1	1	1	1	-1	-1	R_z
B₁	1	-1	1	-1	1	1	-1
B₂	1	-1	1	-1	1	-1	1	z
E₁	2	(2)^1/2	0	-(2)^1/2	-2	0	0	(x, y)
E₂	2	0	-2	0	2	0	0		(x²-y², xy)
E₃	2	-(2)^1/2	0	(2)^1/2	-2	0	0	(R_x, R_y)	(xz, yz)

Product table for D_4d point group

Printable: character table for D_4d product table for D_4d D_4d point group