c6h - Point Group Symmetry Character Tables - Chemistry Online Education

C6H - POINT GROUP SYMMETRY CHARACTER TABLES

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Nonaxial
C₁
C_s
C_i

C_n
C₂
C₃
C₄
C₅
C₆

C_nv
C_2v
C_3v
C_4v
C_5v
C_6v

C_nh
C_2h
C_3h
C_4h
C_5h
C_6h

D_n
D₂
D₃
D₄
D₅
D₆

D_nh
D_2h
D_3h
D_4h
D_5h
D_6h

D_nd
D_2d
D_3d
D_4d
D_5d
D_6d

S_n
S₄
S₆
S₈
S₁₀

Higher
T_d
O_h
I_h

Linear
C_∞v
D_∞h

C_6h Point Group

Abelian, 8(12) irreducible representations

Subgroups of C_6h point group: C_s, C_i, C₂, C₃, C₆, C_2h, C_3h, S₆

Character table for C_6h point group

	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 for C_6h point group

	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

Printable: character table for C_6h product table for C_6h C_6h point group

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