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Point Group Tables of C3v(3m)

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Character Table of the group C3v(3m) *
C3v(3m)#13mfunctions
Mult.-123
A1Γ1111z,x2+y2,z2
A2Γ211-1Jz
EΓ32-10(x,y),(xz,yz),(x2-y2,xy),(Jx,Jy)



Subgroups of the group C3v(3m)
SubgroupOrderIndex
C3v(3m)61
C3(3)32
Cs(m)23
C1(1)16

[ Subduction tables ]

Multiplication Table of irreducible representations of the group C3v(3m)
C3v(3m)A1A2E
A1A1A2E
A2A1E
EA1+A2+E

[ Note: the table is symmetric ]


Symmetrized Products of Irreps
C3v(3m)A1A2E
[A1 x A1]1··
[A2 x A2]1··
[E x E]1·1


Antisymmetrized Products of Irreps
C3v(3m)A1A2E
{A1 x A1}···
{A2 x A2}···
{E x E}·1·


Irreps Decompositions
C3v(3m)A1A2E
V1·1
[V2]2·2
[V3]313
[V4]415
A·11
[A2]2·2
[A3]133
[A4]415
[V2]xV426
[[V2]2]617
{V2}·11
{A2}·11
{[V2]2}235

V ≡ the vector representation
A ≡ the axial representation


IR Selection Rules
IRA1A2E
A1xx
A2xx
Exxx

[ Note: x means allowed ]


Raman Selection Rules
RamanA1A2E
A1xx
A2xx
Exxx

[ Note: x means allowed ]


Irreps Dimensions Irreps of the point group
Subduction of the rotation group D(L) to irreps of the group C3v(3m)
L2L+1A1A2E
011··
131·1
251·2
37212
49213
511214
613324
715325
817326
919436
1021437



* 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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