Bilbao Crystallographic Server bcs Point Group Tables Help

Point Group Tables of C6(6)

Click here to get more detailed information on the symmetry operations

Character Table of the group C6(6) *
C6(6)#16+3+23-6-functions
AΓ1111111z,x2+y2,z2,Jz
BΓ41-11-11-1
1E2
2E2
Γ3
Γ2
1
1
w
w2
w2
w
1
1
w
w2
w2
w
(x2-y2,xy)
2E1
1E1
Γ5
Γ6
1
1
-w2
-w
w
w2
-1
-1
w2
w
-w
-w2
(x,y),(xz,yz),(Jx,Jy)

w = exp(2iπ/3)



Subgroups of the group C6(6)
SubgroupOrderIndex
C6(6)61
C3(3)32
C2(2)23
C1(1)16

[ Subduction tables ]

Multiplication Table of irreducible representations of the group C6(6)
C6(6)AB2E21E11E22E1
AAB2E21E11E22E1
BA1E12E22E11E2
2E21E22E1AB
1E11E2BA
1E22E21E1
2E12E2

[ Note: the table is symmetric ]


Symmetrized Products of Irreps
C6(6)AB2E21E11E22E1
[A x A]1·····
[B x B]1·····
[2E2 x 2E2]····1·
[1E1 x 1E1]····1·
[1E2 x 1E2]··1···
[2E1 x 2E1]··1···


Antisymmetrized Products of Irreps
C6(6)AB2E21E11E22E1
{A x A}······
{B x B}······
{2E2 x 2E2}······
{1E1 x 1E1}······
{1E2 x 1E2}······
{2E1 x 2E1}······


Irreps Decompositions
C6(6)AB2E21E11E22E1
V1··1·1
[V2]2·1111
[V3]221212
[V4]323232
A1··1·1
[A2]2·1111
[A3]221212
[A4]323232
[V2]xV422424
[[V2]2]524343
{V2}1··1·1
{A2}1··1·1
{[V2]2}322323

V ≡ the vector representation
A ≡ the axial representation


IR Selection Rules
IRAB2E21E11E22E1
Axxx
Bxxx
2E2xxx
1E1xxx
1E2xxx
2E1xxx

[ Note: x means allowed ]


Raman Selection Rules
RamanAB2E21E11E22E1
Axxxxx
Bxxxxx
2E2xxxxx
1E1xxxxx
1E2xxxxx
2E1xxxxx

[ Note: x means allowed ]


Irreps Dimensions Irreps of the point group
Subduction of the rotation group D(L) to irreps of the group C6(6)
L2L+1AB2E21E11E22E1
011·····
131··1·1
251·1111
37121111
49122121
511122222
613322222
715322323
817323333
919343333
1021344343



* 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