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Point Group Th

Point Group Th

Character Table

	$\text{E} \,{\text{(1)}}$	$C_3 \,{\text{(8)}}$	$C_2 \,{\text{(3)}}$	$\text{i} \,{\text{(1)}}$	$S_6 \,{\text{(8)}}$	$\sigma_h \,{\text{(3)}}$
$A_g$	$1$	$1$	$1$	$1$	$1$	$1$
$E_g$	$2$	$-1$	$2$	$2$	$-1$	$2$
$T_g$	$3$	$0$	$-1$	$3$	$0$	$-1$
$A_u$	$1$	$1$	$1$	$-1$	$-1$	$-1$
$E_u$	$2$	$-1$	$2$	$-2$	$1$	$-2$
$T_u$	$3$	$0$	$-1$	$-3$	$0$	$1$

Product Table

	$A_g$	$E_g$	$T_g$	$A_u$	$E_u$	$T_u$
$A_g$	$A_g$	$E_g$	$T_g$	$A_u$	$E_u$	$T_u$
$E_g$	$E_g$	$2 A_g+E_g$	$2 T_g$	$E_u$	$2 A_u+E_u$	$2 T_u$
$T_g$	$T_g$	$2 T_g$	$A_g+E_g+2 T_g$	$T_u$	$2 T_u$	$A_u+E_u+2 T_u$
$A_u$	$A_u$	$E_u$	$T_u$	$A_g$	$E_g$	$T_g$
$E_u$	$E_u$	$2 A_u+E_u$	$2 T_u$	$E_g$	$2 A_g+E_g$	$2 T_g$
$T_u$	$T_u$	$2 T_u$	$A_u+E_u+2 T_u$	$T_g$	$2 T_g$	$A_g+E_g+2 T_g$

Implemented Settings

Setting xyz

Details of the Th group in with setting xyz

Operator	Orientation
$\text{E}$	$\{0,0,0\}$ ,
$C_3$	$\{1,1,1\}$ , $\{1,1,-1\}$ , $\{1,-1,1\}$ , $\{-1,1,1\}$ , $\{-1,-1,1\}$ , $\{-1,1,-1\}$ , $\{1,-1,-1\}$ , $\{-1,-1,-1\}$ ,
$C_2$	$\{0,0,1\}$ , $\{0,1,0\}$ , $\{1,0,0\}$ ,
$\text{i}$	$\{0,0,0\}$ ,
$S_6$	$\{1,1,1\}$ , $\{1,1,-1\}$ , $\{1,-1,1\}$ , $\{-1,1,1\}$ , $\{-1,-1,1\}$ , $\{-1,1,-1\}$ , $\{1,-1,-1\}$ , $\{-1,-1,-1\}$ ,
$\sigma _h$	$\{1,0,0\}$ , $\{0,1,0\}$ , $\{0,0,1\}$ ,

Table of several point groups

Return to Main page on Point Groups

Nonaxial groups	C₁	C_s	C_i
C_n groups	C₂	C₃	C₄	C₅	C₆	C₇	C₈
D_n groups	D₂	D₃	D₄	D₅	D₆	D₇	D₈
C_nv groups	C_2v	C_3v	C_4v	C_5v	C_6v	C_7v	C_8v
C_nh groups	C_2h	C_3h	C_4h	C_5h	C_6h
D_nh groups	D_2h	D_3h	D_4h	D_5h	D_6h	D_7h	D_8h
D_nd groups	D_2d	D_3d	D_4d	D_5d	D_6d	D_7d	D_8d
S_n groups	S₂	S₄	S₆	S₈	S₁₀	S₁₂
Cubic groups	T	T_h	T_d	O	O_h	I	I_h
Linear groups	C_{$\infty$ v}	D_{$\infty$ h}

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