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c5h - Point Group Symmetry Character Tables


Nonaxial
C1
Cs
Ci
Cn
C2
C3
C4
C5
C6
Cnv
C2v
C3v
C4v
C5v
C6v
Cnh
C2h
C3h
C4h
C5h
C6h
Dn
D2
D3
D4
D5
D6
Dnh
D2h
D3h
D4h
D5h
D6h
Dnd
D2d
D3d
D4d
D5d
D6d
Sn
S4
S6
S8
S10
Higher
Td
Oh
Ih
Linear
C∞v
D∞h

C5h Point Group

Abelian, 6(10) irreducible representations
Subgroups of C5h point group: Cs, C5

Character table for C5h point group
E C5 (C5)2 (C5)3 (C5)4 σh S5 (S5)7 (S5)3 (S5)9 linear,
rotations
quadratic
A' 1 1 1 1 1 1 1 1 1 1 Rz x2+y2, z2
E'1 1
1
e
e*
e2
e2*
e2*
e2
e*
e
1
1
e
e*
e2
e2*
e2*
e2
e*
e
x+iy
x-iy
E'2 1
1
e2
e2*
e*
e
e
e*
e2*
e2
1
1
e2
e2*
e*
e
e
e*
e2*
e2
(x2-y2, xy)
A'' 1 1 1 1 1 -1 -1 -1 -1 -1 z
E''1 1
1
e
e*
e2
e2*
e2*
e2
e*
e
-1
-1
-e
-e*
-e2
-e2*
-e2*
-e2
-e*
-e
Rx+iRy
Rx-iRy
(xz, yz)
E''2 1
1
e2
e2*
e*
e
e
e*
e2*
e2
-1
-1
-e2
-e2*
-e*
-e
-e
-e*
-e2*
-e2
e = exp(2πi/5)

Product table for C5h point group
 A'E1'E2'A''E1''E2''
A'A'E1'E2'A''E1''E2''
E1'E1'2A'+E2'E1'+E2'E1''2A''+E2''E1''+E2''
E2'E2'E1'+E2'2A'+E1'E2''E1''+E2''2A''+E1''
A''A''E1''E2''A'E1'E2'
E1''E1''2A''+E2''E1''+E2''E1'2A'+E2'E1'+E2'
E2''E2''E1''+E2''2A''+E1''E2'E1'+E2'2A'+E1'

Printable C5h point group
Printable character table for C5h point group
Printable product table for C5h point group

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