d4h - Point Group Symmetry Character Tables - Chemistry Online Education

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Linear
C_∞v
D_∞h

D_4h Point Group

not Abelian, 10(12) irreducible representations

Subgroups of D_4h point group: C_s, C_i, C₂, C₄, D₂, D₄, C_2v, C_4v, C_2h, C_4h, D_2h, D_2d, S₄

Character table for D_4h point group

	E	2C₄ (z)	C₂	2C'₂	2C''₂	i	2S₄	σ_h	2σ_v	2σ_d	linears, rotations	quadratic
A_1g	1	1	1	1	1	1	1	1	1	1		x²+y², z²
A_2g	1	1	1	-1	-1	1	1	1	-1	-1	R_z
B_1g	1	-1	1	1	-1	1	-1	1	1	-1		x²-y²
B_2g	1	-1	1	-1	1	1	-1	1	-1	1		xy
E_g	2	0	-2	0	0	2	0	-2	0	0	(R_x, R_y)	(xz, yz)
A_1u	1	1	1	1	1	-1	-1	-1	-1	-1
A_2u	1	1	1	-1	-1	-1	-1	-1	1	1	z
B_1u	1	-1	1	1	-1	-1	1	-1	-1	1
B_2u	1	-1	1	-1	1	-1	1	-1	1	-1
E_u	2	0	-2	0	0	-2	0	2	0	0	(x, y)

Product table for D_4h point group

Printable: character table for D_4h product table for D_4h D_4h point group