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Cn group - C8


C8

Symmetry elements for the group

Spectroscopy active component

E

C8

C4

(C8)3

C2

(C8)5

(C4)3

(C8)7

Microwave

IR

Raman

Symmetry label

A

1

1

1

1

1

1

1

1

Rz

z,

x2+y2, z2

B

1

-1

1

-1

1

-1

1

-1

 

 

 

E1

1

e

i

-e*

-1

-e

-i

e*

Rx+iRy
Rx-iRy

x+iy
x-iy

(xz, yz)

1

e*

-i

-e

-1

-e*

i

e

E2

1

i

-1

-i

1

i

-1

-i

 

 

(x2-y2, xy)

1

-i

-1

i

1

-i

-1

i

E3

1

-e

i

e*

-1

e

-i

-e*

 

 

 

1

-e*

-i

e

-1

e*

i

-e

 Where e = exp(2pi/8)

 

C2 is the simplest point group that there is. An examples of this is:


Also contained in this group (Cn group) is:  C2  C3  C4  C5 C6  C7