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C3h point group
Abelian, 4(6) irreducible representations
Subgroups: Cs, C3

Character table
E C3(z) (C3)2 σh S3 (S3)5
linear functions,
rotations
quadratic
functions
A' 1 1 1 1 1 1 Rz x2+y2, z2
E' 1
1
e
e*
e*
e
1
1
e
e*
e*
e
x+iy
x-iy
(x2-y2, xy)
A'' 1 1 1 -1 -1 -1 z
E'' 1
1
e
e*
e*
e
-1
-1
-e
-e*
-e*
-e
Rx+iRy
Rx-iRy
(xz, yz)

Product table
 A'E'A''E''
A'A'E'A''E''
E'E'2A'+E'E''2A''+E''
A''A''E''A'E'
E''E''2A''+E''E'2A'+E'

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