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Point Group Tables of T(23)

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Character Table of the group T(23) *
T(23)#123+3-functions
Mult.-1344
AΓ11111x2+y2+z2
1E
2E
Γ2
Γ3
1
1
1
1
w
w2
w2
w
(2z2-x2-y2,x2-y2)
TΓ43-100(x,y,z),(xy,xz,yz),(Jx,Jy,Jz)

w = exp(2iπ/3)



Subgroups of the group T(23)
SubgroupOrderIndex
T(23)121
C3(3)34
D2(222)43
C2(2)26
C1(1)112

[ Subduction tables ]

Multiplication Table of irreducible representations of the group T(23)
T(23)A1E2ET
AA1E2ET
1E2EAT
2E1ET
TA+1E+2E+2T

[ Note: the table is symmetric ]


Symmetrized Products of Irreps
T(23)A1E2ET
[A x A]1···
[1E x 1E]··1·
[2E x 2E]·1··
[T x T]1111


Antisymmetrized Products of Irreps
T(23)A1E2ET
{A x A}····
{1E x 1E}····
{2E x 2E}····
{T x T}···1


Irreps Decompositions
T(23)A1E2ET
V···1
[V2]1111
[V3]1··3
[V4]2223
A···1
[A2]1111
[A3]1··3
[A4]2223
[V2]xV1115
[[V2]2]3334
{V2}···1
{A2}···1
{[V2]2}1114

V ≡ the vector representation
A ≡ the axial representation


IR Selection Rules
IRA1E2ET
Ax
1Ex
2Ex
Txxxx

[ Note: x means allowed ]


Raman Selection Rules
RamanA1E2ET
Axxxx
1Exxxx
2Exxxx
Txxxx

[ Note: x means allowed ]


Irreps Dimensions Irreps of the point group
Subduction of the rotation group D(L) to irreps of the group T(23)
L2L+1A1E2ET
011···
13···1
25·111
371··2
491112
511·113
6132113
7151114
8171224
9192115
10212225



* 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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