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Point Group Tables of D2(222)

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Character Table of the group D2(222) *
D2(222)#12z2y2xfunctions
AΓ11111x2,y2,z2
B1Γ311-1-1z,xy,Jz
B2Γ21-11-1y,xz,Jy
B3Γ41-1-11x,yz,Jx



Subgroups of the group D2(222)
SubgroupOrderIndex
D2(222)41
C2(2)22
C1(1)14

[ Subduction tables ]

Multiplication Table of irreducible representations of the group D2(222)
D2(222)AB1B2B3
AAB1B2B3
B1AB3B2
B2AB1
B3A

[ Note: the table is symmetric ]


Symmetrized Products of Irreps
D2(222)AB1B2B3
[A x A]1···
[B1 x B1]1···
[B2 x B2]1···
[B3 x B3]1···


Antisymmetrized Products of Irreps
D2(222)AB1B2B3
{A x A}····
{B1 x B1}····
{B2 x B2}····
{B3 x B3}····


Irreps Decompositions
D2(222)AB1B2B3
V·111
[V2]3111
[V3]1333
[V4]6333
A·111
[A2]3111
[A3]1333
[A4]6333
[V2]xV3555
[[V2]2]9444
{V2}·111
{A2}·111
{[V2]2}3444

V ≡ the vector representation
A ≡ the axial representation


IR Selection Rules
IRAB1B2B3
Axxx
B1xxx
B2xxx
B3xxx

[ Note: x means allowed ]


Raman Selection Rules
RamanAB1B2B3
Axxxx
B1xxxx
B2xxxx
B3xxxx

[ Note: x means allowed ]


Irreps Dimensions Irreps of the point group
Subduction of the rotation group D(L) to irreps of the group D2(222)
L2L+1AB1B2B3
011···
13·111
252111
371222
493222
5112333
6134333
7153444
8175444
9194555
10216555



* 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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