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

Character table
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

Product table
 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'

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