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s6 - Point Group Symmetry Character Tables

S6 Point Group

Abelian, 4(6) irreducible representations
Subgroups of S6 point group: Ci, C3

Character table for S6 point group

EC3(z)(C3)2i(S6)5S6linear,
rotations
quadratic
Ag111111Rzx2+y2, z2
Eg1
1
e
e*
e*
e
1
1
e
e*
e*
e
Rx+iRy
Rx-iRy
(x2-y2, xy) (xz, yz)
Au111-1-1-1z
Eu1
1
e
e*
e*
e
-1
-1
-e
-e*
-e*
-e
x+iy
x-iy
e = exp(2πi/3)

Product table for S6 point group

 AgEgAuEu
AgAgEgAuEu
EgEg2Ag+EgAu2Au+Eu
AuAuEuAgEg
EuAu2Au+EuEg2Ag+Eg

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

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