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Point Group Tables of Cs(m)

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Character Table of the group Cs(m) *
Cs(m)#1mfunctions
A'Γ111x,y,x2,y2,z2,xy,Jz
A''Γ21-1z,xz,yz,Jx,Jy



Subgroups of the group Cs(m)
SubgroupOrderIndex
Cs(m)21
C1(1)12

[ Subduction tables ]

Multiplication Table of irreducible representations of the group Cs(m)
Cs(m)A'A''
A'A'A''
A''A'

[ Note: the table is symmetric ]


Symmetrized Products of Irreps
Cs(m)A'A''
[A' x A']1·
[A'' x A'']1·


Antisymmetrized Products of Irreps
Cs(m)A'A''
{A' x A'}··
{A'' x A''}··


Irreps Decompositions
Cs(m)A'A''
V21
[V2]42
[V3]64
[V4]96
A12
[A2]42
[A3]46
[A4]96
[V2]xV108
[[V2]2]138
{V2}12
{A2}12
{[V2]2}78

V ≡ the vector representation
A ≡ the axial representation


IR Selection Rules
IRA'A''
A'xx
A''xx

[ Note: x means allowed ]


Raman Selection Rules
RamanA'A''
A'xx
A''xx

[ Note: x means allowed ]


Irreps Dimensions Irreps of the point group
Subduction of the rotation group D(L) to irreps of the group Cs(m)
L2L+1A'A''
011·
1321
2532
3743
4954
51165
61376
71587
81798
919109
10211110



* George F. Koster, John O. Dimmock, Robert G. Wheeler, Hermann Statz (1963). Properties of the thirty-two point groups. Published by the M.I.T. press, Cambridge, Massachusetts.
* Simon L. Altmann and Peter Herzig (1994). Point-Group Theory Tables. Oxford Science Publications.


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