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Point Group Tables of Td(-43m)

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Character Table of the group Td(-43m) *
Td(-43m)#132-4mfunctions
Mult.-18366
A1Γ111111x2+y2+z2
A2Γ2111-1-1
EΓ32-1200(2z2-x2-y2,x2-y2)
T1Γ430-11-1(Jx,Jy,Jz)
T2Γ530-1-11(x,y,z),(xy,xz,yz)



Subgroups of the group Td(-43m)
SubgroupOrderIndex
Td(-43m)241
T(23)122
C3v(3m)64
C3(3)38
D2d(-42m)83
S4(-4)46
C2v(mm2)46
D2(222)46
C2(2)212
Cs(m)212
C1(1)124

[ Subduction tables ]

Multiplication Table of irreducible representations of the group Td(-43m)
Td(-43m)A1A2ET1T2
A1A1A2ET1T2
A2A1ET2T1
EA1+A2+ET1+T2T1+T2
T1A1+E+T1+T2A2+E+T1+T2
T2A1+E+T1+T2

[ Note: the table is symmetric ]


Symmetrized Products of Irreps
Td(-43m)A1A2ET1T2
[A1 x A1]1····
[A2 x A2]1····
[E x E]1·1··
[T1 x T1]1·1·1
[T2 x T2]1·1·1


Antisymmetrized Products of Irreps
Td(-43m)A1A2ET1T2
{A1 x A1}·····
{A2 x A2}·····
{E x E}·1···
{T1 x T1}···1·
{T2 x T2}···1·


Irreps Decompositions
Td(-43m)A1A2ET1T2
V····1
[V2]1·1·1
[V3]1··12
[V4]2·212
A···1·
[A2]1·1·1
[A3]·1·21
[A4]2·212
[V2]xV1·123
[[V2]2]3·313
{V2}···1·
{A2}···1·
{[V2]2}·1122

V ≡ the vector representation
A ≡ the axial representation


IR Selection Rules
IRA1A2ET1T2
A1x
A2x
Exx
T1xxxx
T2xxxx

[ Note: x means allowed ]


Raman Selection Rules
RamanA1A2ET1T2
A1xxx
A2xxx
Exxxxx
T1xxxx
T2xxxx

[ Note: x means allowed ]


Irreps Dimensions Irreps of the point group
Subduction of the rotation group D(L) to irreps of the group Td(-43m)
L2L+1A1A2ET1T2
011····
13····1
25··1·1
371··11
491·111
511··112
61311112
7151·122
8171·222
91911123
102111223



* 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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