Character Tables

C_6h Character Table

C_6h	E	C₆	C₃	C₂	C₃²	C₆⁵	i	S₃⁵	S₆⁵	σ_h	S₆	S₃	Linear Functions	Quadratic Functions
A_g	1	1	1	1	1	1	1	1	1	1	1	1	R_z	x² + y², z²
B_g	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1
E_1g	1	ε	-ε*	-1	-ε	ε*	1	ε	-ε*	-1	-ε	ε*	(R_x,R_y)	(xz,yz)
E_1g	1	ε*	-ε	-1	-ε*	ε	1	ε*	-ε	-1	-ε*	ε	(R_x,R_y)	(xz,yz)
E_2g	1	-ε*	-ε	1	-ε*	-ε	1	-ε*	-ε	1	-ε*	-ε		(x² - y²,xy)
E_2g	1	-ε	-ε*	1	-ε	-ε*	1	-ε	-ε*	1	-ε	-ε*		(x² - y²,xy)
A_u	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	z
B_u	1	-1	1	-1	1	-1	-1	1	-1	1	-1	1
E_1u	1	ε	-ε*	-1	-ε	ε*	-1	-ε	ε*	1	ε	-ε*	(x,y)
E_1u	1	ε*	-ε	-1	-ε*	ε	-1	-ε*	ε	1	ε*	-ε	(x,y)
E_2u	1	-ε*	-ε	1	-ε*	-ε	-1	ε*	ε	-1	ε*	ε
E_2u	1	-ε	-ε*	1	-ε	-ε*	-1	ε	ε*	-1	ε	ε*

ε = e^(2πi)/6, ε* = e^(2π-i)/6
i = -1^½

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