d6h - Point Group Symmetry Character Tables - Chemistry Online Education

D6H - 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

D_6h Point Group

Abelian, 12(16) irreducible representations

Subgroups of D_6h point group: C_s, C_i, C₂, C₃, C₆, D₂, D₃, D₆, C_2v, C_3v, C_6v, C_2h, C_3h, C_6h, D_2h, D_3h, D_3d, S₆

Character table for D_6h point group

	E	2C₆	2C₃	C₂	3C'₂	3C''₂	i	2S₃	2S₆	σ_h	3σ_d	3σ_v	Linear, rotations	Quadratic
A_1g	1	1	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	-1	-1	R_z
B_1g	1	-1	1	-1	1	-1	1	-1	1	-1	1	-1
B_2g	1	-1	1	-1	-1	1	1	-1	1	-1	-1	1
E_1g	2	1	-1	-2	0	0	2	1	-1	-2	0	0	(R_x, R_y)	(xz, yz)
E_2g	2	-1	-1	2	0	0	2	-1	-1	2	0	0		(x²-y², xy)
A_1u	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1
A_2u	1	1	1	1	-1	-1	-1	-1	-1	-1	1	1	z
B_1u	1	-1	1	-1	1	-1	-1	1	-1	1	-1	1
B_2u	1	-1	1	-1	-1	1	-1	1	-1	1	1	-1
E_1u	2	1	-1	-2	0	0	-2	-1	1	2	0	0	(x, y)
E_2u	2	-1	-1	2	0	0	-2	1	1	-2	0	0

Product table for D_6h point group

	A_1g	A_2g	B_1g	B_2g	E_1g	E_2g	A_1u	A_2u	B_1u	B_2u	E_1u	E_2u
A_1g	A_1g	A_2g	B_1g	B_2g	E_1g	E_2g	A_1u	A_2u	B_1u	B_2u	E_1u	E_2u
A_2g	A_2g	A_1g	B_2g	B_1g	E_1g	E_2g	A_2u	A_1u	B_2u	B_1u	E_1u	E_2u
B_1g	B_1g	B_2g	A_1g	A_2g	E_2g	E_1g	B_1u	B_2u	A_1u	A_2u	E_2u	E_1u
B_2g	B_2g	B_1g	A_2g	A_1g	E_2g	E_1g	B_2u	B_1u	A_2u	A_1u	E_2u	E_1u
E_1g	E_1g	E_1g	E_2g	E_2g	A_1g+A_2g+E_2g	B_1g+B_2g+E_1g	E_1u	E_1u	E_2u	E_2u	A_1u+A_2u+E_2u	B_1u+B_2u+E_1u
E_2g	E_2g	E_2g	E_1g	E_1g	B_1g+B_2g+E_1g	A_1g+A_2g+E_2g	E_2u	E_2u	E_1u	E_1u	B_1u+B_2u+E_1u	A_1u+A_2u+E_2u
A_1u	A_1u	A_2u	B_1u	B_2u	E_1u	E_2u	A_1g	A_2g	B_1g	B_2g	E_1g	E_2g
A_2u	A_2u	A_1u	B_2u	B_1u	E_1u	E_2u	A_2g	A_1g	B_2g	B_1g	E_1g	E_2g
B_1u	B_1u	B_2u	A_1u	A_2u	E_2u	E_1u	B_1g	B_2g	A_1g	A_2g	E_2g	E_1g
B_2u	B_2u	B_1u	A_2u	A_1u	E_2u	E_1u	B_2g	B_1g	A_2g	A_1g	E_2g	E_1g
E_1u	E_1u	E_1u	E_2u	E_2u	A_1u+A_2u+E_2u	B_1u+B_2u+E_1u	E_1g	E_1g	E_2g	E_2g	A_1g+A_2g+E_2g	B_1g+B_2g+E_1g
E_2u	E_2u	E_2u	E_1u	E_1u	B_1u+B_2u+E_1u	A_1u+A_2u+E_2u	E_2g	E_2g	E_1g	E_1g	B_1g+B_2g+E_1g	A_1g+A_2g+E_2g

Printable: character table for D_6h product table for D_6h D_6h point group

Page d6h - Point Group Symmetry Character Tables from the Chemical Portal