Character Tables

D_8d Character Table

D_8d	E	2S₁₆	2C₈	2S₁₆³	2C₄	2S₁₆⁵	2C₈³	2S₁₆⁷	C₂	8C₂'	8σ_d	Linear Functions	Quadratic Functions
A₁	1	1	1	1	1	1	1	1	1	1	1		x² + y², z²
A₂	1	1	1	1	1	1	1	1	1	-1	-1	R_z
B₁	1	-1	1	-1	1	-1	1	-1	1	1	-1
B₂	1	-1	1	-1	1	-1	1	-1	1	-1	1	z
E₁	2	2 cos (1π/8)	2^½	2 cos (3π/8)	0	-2 cos (3π/8)	-(2^½)	-2 cos (1π/8)	-2	0	0	(x,y)
E₂	2	2^½	0	-(2^½)	-2	-(2^½)	0	2^½	2	0	0		(x² - y²,xy)
E₃	2	2 cos (3π/8)	-(2^½)	-2 cos (1π/8)	0	2 cos (1π/8)	2^½	-2 cos (3π/8)	-2	0	0
E₄	2	0	-2	0	2	0	-2	0	2	0	0
E₅	2	-2 cos (3π/8)	-(2^½)	2 cos (1π/8)	0	-2 cos (1π/8)	2^½	2 cos (3π/8)	-2	0	0
E₆	2	-(2^½)	0	2^½	-2	2^½	0	-(2^½)	2	0	0
E₇	2	-2 cos (1π/8)	2^½	-2 cos (3π/8)	0	2 cos (3π/8)	-(2^½)	2 cos (1π/8)	-2	0	0	(R_x,R_y)	(xz,yz)

Back to Common Character Tables in Chemistry

Back to Chemistry Resources