Bilbao Crystallographic Server bcs Point Group Tables Help

Point Group Tables of D3(32)

Click here to get more detailed information on the symmetry operations

Character Table of the group D3(32) *
D3(32)#132functions
Mult.-123
A1Γ1111x2+y2,z2
A2Γ211-1z,Jz
EΓ32-10(x,y),(xz,yz),(x2-y2,xy),(Jx,Jy)



Subgroups of the group D3(32)
SubgroupOrderIndex
D3(32)61
C3(3)32
C2(2)23
C1(1)16

[ Subduction tables ]

Multiplication Table of irreducible representations of the group D3(32)
D3(32)A1A2E
A1A1A2E
A2A1E
EA1+A2+E

[ Note: the table is symmetric ]


Symmetrized Products of Irreps
D3(32)A1A2E
[A1 x A1]1··
[A2 x A2]1··
[E x E]1·1


Antisymmetrized Products of Irreps
D3(32)A1A2E
{A1 x A1}···
{A2 x A2}···
{E x E}·1·


Irreps Decompositions
D3(32)A1A2E
V·11
[V2]2·2
[V3]133
[V4]415
A·11
[A2]2·2
[A3]133
[A4]415
[V2]xV246
[[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 D3(32)
L2L+1A1A2E
011··
13·11
251·2
37122
49213
511124
613324
715235
817326
919346
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.


Bilbao Crystallographic Server
http://www.cryst.ehu.es
For comments, please mail to
cryst@wm.lc.ehu.es