c6h point group

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C_6h point group

Abelian, 8(12) irreducible representations

Subgroups: C_s, C_i, C₂, C₃, C₆, C_2h, C_3h, S₆

**Character table**
	E	C₆(z)	C₃	C₂	(C₃)²	(C₆)⁵	i	(S₃)⁵	(S₆)⁵	σ_h	S₆	S₃	linear, rotations	quadratic
A_g	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 1	e e^*	-e^* -e	-1 -1	-e -e^*	e^* e	1 1	e e^*	-e^* -e	-1 -1	-e -e^*	e^* e	R_x+iR_y R_x-iR_y	(xz, yz)
E_2g	1 1	-e^* -e	-e -e^*	1 1	-e^* -e	-e -e^*	1 1	-e^* -e	-e -e^*	1 1	-e^* -e	-e -e^*		(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 1	e e^*	-e^* -e	-1 -1	-e -e^*	e^* e	-1 -1	-e -e^*	e^* e	1 1	e e^*	-e^* -e	x+iy x-iy
E_2u	1 1	-e^* -e	-e -e^*	1 1	-e^* -e	-e -e^*	-1 -1	e^* e	e e^*	-1 -1	e^* e	e e^*

**Product table**
	A_g	B_g	E_1g	E_2g	A_u	B_u	E_1u	E_2u
A_g	A_g	B_g	E_1g	E_2g	A_u	B_u	E_1u	E_2u
B_g	B_g	A_g	E_2g	E_1g	B_u	A_u	E_2u	E_1u
E_1g	E_1g	E_2g	2A_g+E_2g	2B_g+E_1g	E_1u	E_2u	2A_u+E_2u	2B_u+E_1u
E_2g	E_2g	E_1g	2B_g+E_1g	2A_g+E_2g	E_2u	E_1u	2B_u+E_1u	2A_u+E_2u
A_u	A_u	B_u	E_1u	E_2u	A_g	B_g	E_1g	E_2g
B_u	B_u	A_u	E_2u	E_1u	B_g	A_g	E_2g	E_1g
E_1u	E_1u	E_2u	2A_u+E_2u	2B_u+E_1u	E_1g	E_2g	2A_g+E_2g	2B_g+E_1g
E_2u	E_2u	E_1u	2B_u+E_1u	2A_u+E_2u	E_2g	E_1g	2B_g+E_1g	2A_g+E_2g

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