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Point Group Tables of C2(2)

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Character Table of the group C2(2) *
C2(2)#12functions
AΓ111z,x2,y2,z2,xy,Jz
BΓ21-1x,y,xz,yz,Jx,Jy



Subgroups of the group C2(2)
SubgroupOrderIndex
C2(2)21
C1(1)12

[ Subduction tables ]

Multiplication Table of irreducible representations of the group C2(2)
C2(2)AB
AAB
BA

[ Note: the table is symmetric ]


Symmetrized Products of Irreps
C2(2)AB
[A x A]1·
[B x B]1·


Antisymmetrized Products of Irreps
C2(2)AB
{A x A}··
{B x B}··


Irreps Decompositions
C2(2)AB
V12
[V2]42
[V3]46
[V4]96
A12
[A2]42
[A3]46
[A4]96
[V2]xV810
[[V2]2]138
{V2}12
{A2}12
{[V2]2}78

V ≡ the vector representation
A ≡ the axial representation


IR Selection Rules
IRAB
Axx
Bxx

[ Note: x means allowed ]


Raman Selection Rules
RamanAB
Axx
Bxx

[ Note: x means allowed ]


Irreps Dimensions Irreps of the point group
Subduction of the rotation group D(L) to irreps of the group C2(2)
L2L+1AB
011·
1312
2532
3734
4954
51156
61376
71578
81798
919910
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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