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Point Group Tables of C6v(6mm)

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Character Table of the group C6v(6mm) *
C6v(6mm)#1236mdmvfunctions
Mult.-112233
A1Γ1111111z,x2+y2,z2
A2Γ21111-1-1Jz
B1Γ31-11-11-1
B2Γ41-11-1-11
E2Γ622-1-100(x2-y2,xy)
E1Γ52-2-1100(x,y),(xz,yz),(Jx,Jy)



Subgroups of the group C6v(6mm)
SubgroupOrderIndex
C6v(6mm)121
C6(6)62
C3v(3m)62
C3(3)34
C2v(mm2)43
C2(2)26
Cs(m)26
C1(1)112

[ Subduction tables ]

Multiplication Table of irreducible representations of the group C6v(6mm)
C6v(6mm)A1A2B1B2E2E1
A1A1A2B1B2E2E1
A2A1B2B1E2E1
B1A1A2E1E2
B2A1E1E2
E2A1+A2+E2B1+B2+E1
E1A1+A2+E2

[ Note: the table is symmetric ]


Symmetrized Products of Irreps
C6v(6mm)A1A2B1B2E2E1
[A1 x A1]1·····
[A2 x A2]1·····
[B1 x B1]1·····
[B2 x B2]1·····
[E2 x E2]1···1·
[E1 x E1]1···1·


Antisymmetrized Products of Irreps
C6v(6mm)A1A2B1B2E2E1
{A1 x A1}······
{A2 x A2}······
{B1 x B1}······
{B2 x B2}······
{E2 x E2}·1····
{E1 x E1}·1····


Irreps Decompositions
C6v(6mm)A1A2B1B2E2E1
V1····1
[V2]2···11
[V3]2·1112
[V4]3·1132
A·1···1
[A2]2···11
[A3]·21112
[A4]3·1132
[V2]xV311124
[[V2]2]5·1143
{V2}·1···1
{A2}·1···1
{[V2]2}121123

V ≡ the vector representation
A ≡ the axial representation


IR Selection Rules
IRA1A2B1B2E2E1
A1xx
A2xx
B1xx
B2xx
E2xxxx
E1xxxx

[ Note: x means allowed ]


Raman Selection Rules
RamanA1A2B1B2E2E1
A1xxx
A2xxx
B1xxx
B2xxx
E2xxxxxx
E1xxxxxx

[ Note: x means allowed ]


Irreps Dimensions Irreps of the point group
Subduction of the rotation group D(L) to irreps of the group C6v(6mm)
L2L+1A1A2B1B2E2E1
011·····
131····1
251···11
371·1111
491·1121
5111·1122
613211122
715211123
817211133
919212233
1021212243



* 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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