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Point Group Tables of C3h(-6)

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Character Table of the group C3h(-6) *
C3h(-6)#13+3-m-6+-6-functions
A'Γ1111111x2+y2,z2,Jz
A''Γ4111-1-1-1z
2E'
1E'
Γ2
Γ3
1
1
w
w2
w2
w
1
1
w
w2
w2
w
(x,y),(x2-y2,xy)
2E''
1E''
Γ5
Γ6
1
1
w
w2
w2
w
-1
-1
-w
-w2
-w2
-w
(xz,yz),(Jx,Jy)

w = exp(2iπ/3)



Subgroups of the group C3h(-6)
SubgroupOrderIndex
C3h(-6)61
C3(3)32
Cs(m)23
C1(1)16

[ Subduction tables ]

Multiplication Table of irreducible representations of the group C3h(-6)
C3h(-6)A'A''1E'1E''2E'2E''
A'A'A''1E'1E''2E'2E''
A''A'1E''1E'2E''2E'
1E'2E'2E''A'A''
1E''2E'A''A'
2E'1E'1E''
2E''1E'

[ Note: the table is symmetric ]


Symmetrized Products of Irreps
C3h(-6)A'A''1E'1E''2E'2E''
[A' x A']1·····
[A'' x A'']1·····
[1E' x 1E']····1·
[1E'' x 1E'']····1·
[2E' x 2E']··1···
[2E'' x 2E'']··1···


Antisymmetrized Products of Irreps
C3h(-6)A'A''1E'1E''2E'2E''
{A' x A'}······
{A'' x A''}······
{1E' x 1E'}······
{1E'' x 1E''}······
{2E' x 2E'}······
{2E'' x 2E''}······


Irreps Decompositions
C3h(-6)A'A''1E'1E''2E'2E''
V·11·1·
[V2]2·1111
[V3]222121
[V4]323232
A1··1·1
[A2]2·1111
[A3]221212
[A4]323232
[V2]xV244242
[[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
IRA'A''1E'1E''2E'2E''
A'xxx
A''xxx
1E'xxx
1E''xxx
2E'xxx
2E''xxx

[ Note: x means allowed ]


Raman Selection Rules
RamanA'A''1E'1E''2E'2E''
A'xxxxx
A''xxxxx
1E'xxxxx
1E''xxxxx
2E'xxxxx
2E''xxxxx

[ Note: x means allowed ]


Irreps Dimensions Irreps of the point group
Subduction of the rotation group D(L) to irreps of the group C3h(-6)
L2L+1A'A''1E'1E''2E'2E''
011·····
13·11·1·
251·1111
37211111
49122121
511212222
613322222
715233232
817323333
919433333
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.


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