Table of Contents

Point Group C5

Point Group C5

Character Table

$ $	$ \text{E} \,{\text{(1)}} $	$ C_5 \,{\text{(2)}} $	$ C_5^2{} \,{\text{(2)}} $
$ \text{A} $	$ 1 $	$ 1 $	$ 1 $
$ E_1 $	$ 2 $	$ \frac{1}{2} \left(-1+\sqrt{5}\right) $	$ \frac{1}{2} \left(-1-\sqrt{5}\right) $
$ E_2 $	$ 2 $	$ \frac{1}{2} \left(-1-\sqrt{5}\right) $	$ \frac{1}{2} \left(-1+\sqrt{5}\right) $

Product Table

$ $	$ \text{A} $	$ E_1 $	$ E_2 $
$ \text{A} $	$ \text{A} $	$ E_1 $	$ E_2 $
$ E_1 $	$ E_1 $	$ 2 \text{A}+E_2 $	$ E_1+E_2 $
$ E_2 $	$ E_2 $	$ E_1+E_2 $	$ 2 \text{A}+E_1 $

Implemented Settings

Setting X

Details of the C5 group in with setting X

Operator	Orientation
$\text{E}$	$\{0,0,0\}$ ,
$C_5$	$\{1,0,0\}$ , $\{-1,0,0\}$ ,
$C_5^2$	$\{1,0,0\}$ , $\{-1,0,0\}$ ,

Setting Y

Details of the C5 group in with setting Y

Operator	Orientation
$\text{E}$	$\{0,0,0\}$ ,
$C_5$	$\{0,1,0\}$ , $\{0,-1,0\}$ ,
$C_5^2$	$\{0,1,0\}$ , $\{0,-1,0\}$ ,

Setting Z

Details of the C5 group in with setting Z

Operator	Orientation
$\text{E}$	$\{0,0,0\}$ ,
$C_5$	$\{0,0,1\}$ , $\{0,0,-1\}$ ,
$C_5^2$	$\{0,0,1\}$ , $\{0,0,-1\}$ ,

Table of several point groups

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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