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Point Group Tables of C1(1)

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Character Table of the group C1(1) *
C1(1)#1
AΓ11



Subgroups of the group C1(1)
SubgroupOrderIndex
C1(1)11

[ Subduction tables ]

Multiplication Table of irreducible representations of the group C1(1)
C1(1)A
AA

[ Note: the table is symmetric ]


Symmetrized Products of Irreps
C1(1)A
[A x A]1


Antisymmetrized Products of Irreps
C1(1)A
{A x A}·


Irreps Decompositions
C1(1)A
V3
[V2]6
[V3]10
[V4]15
A3
[A2]6
[A3]10
[A4]15
[V2]xV18
[[V2]2]21
{V2}3
{A2}3
{[V2]2}15

V ≡ the vector representation
A ≡ the axial representation


IR Selection Rules
IRA
Ax

[ Note: x means allowed ]


Raman Selection Rules
RamanA
Ax

[ Note: x means allowed ]


Irreps Dimensions Irreps of the point group
Subduction of the rotation group D(L) to irreps of the group C1(1)
L2L+1A
011
133
255
377
499
51111
61313
71515
81717
91919
102121



* 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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