Bilbao Crystallographic Server bcs Point Group Tables Help

Point Group Tables of C3(3)

Click here to get more detailed information on the symmetry operations

Character Table of the group C3(3) *
C3(3)#13+3-functions
AΓ1111z,x2+y2,z2,Jz
1E
2E
Γ3
Γ2
1
1
w2
w
w
w2
(x,y),(xz,yz),(x2-y2,xy),(Jx,Jy)

w = exp(2iπ/3)



Subgroups of the group C3(3)
SubgroupOrderIndex
C3(3)31
C1(1)13

[ Subduction tables ]

Multiplication Table of irreducible representations of the group C3(3)
C3(3)A1E2E
AA1E2E
1E2EA
2E1E

[ Note: the table is symmetric ]


Symmetrized Products of Irreps
C3(3)A1E2E
[A x A]1··
[1E x 1E]··1
[2E x 2E]·1·


Antisymmetrized Products of Irreps
C3(3)A1E2E
{A x A}···
{1E x 1E}···
{2E x 2E}···


Irreps Decompositions
C3(3)A1E2E
V111
[V2]222
[V3]433
[V4]555
A111
[A2]222
[A3]433
[A4]555
[V2]xV666
[[V2]2]777
{V2}111
{A2}111
{[V2]2}555

V ≡ the vector representation
A ≡ the axial representation


IR Selection Rules
IRA1E2E
Axxx
1Exxx
2Exxx

[ Note: x means allowed ]


Raman Selection Rules
RamanA1E2E
Axxx
1Exxx
2Exxx

[ Note: x means allowed ]


Irreps Dimensions Irreps of the point group
Subduction of the rotation group D(L) to irreps of the group C3(3)
L2L+1A1E2E
011··
13111
25122
37322
49333
511344
613544
715555
817566
919766
1021777



* 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