Bilbao Crystallographic Server bcs Point Group Tables Help

Point Group Tables of C2h(2/m)

Click here to get more detailed information on the symmetry operations

Character Table of the group C2h(2/m) *
C2h(2/m)#12-1mfunctions
AgΓ1+1111x2,y2,z2,xy,Jz
BgΓ2+1-11-1xz,yz,Jx,Jy
AuΓ1-11-1-1z
BuΓ2-1-1-11x,y



Subgroups of the group C2h(2/m)
SubgroupOrderIndex
C2h(2/m)41
C2(2)22
Cs(m)22
Ci(-1)22
C1(1)14

[ Subduction tables ]

Multiplication Table of irreducible representations of the group C2h(2/m)
C2h(2/m)AgAuBgBu
AgAgAuBgBu
AuAgBuBg
BgAgAu
BuAg

[ Note: the table is symmetric ]


Symmetrized Products of Irreps
C2h(2/m)AgAuBgBu
[Ag x Ag]1···
[Au x Au]1···
[Bg x Bg]1···
[Bu x Bu]1···


Antisymmetrized Products of Irreps
C2h(2/m)AgAuBgBu
{Ag x Ag}····
{Au x Au}····
{Bg x Bg}····
{Bu x Bu}····


Irreps Decompositions
C2h(2/m)AgAuBgBu
V·1·2
[V2]4·2·
[V3]·4·6
[V4]9·6·
A1·2·
[A2]4·2·
[A3]4·6·
[A4]9·6·
[V2]xV·8·10
[[V2]2]13·8·
{V2}1·2·
{A2}1·2·
{[V2]2}7·8·

V ≡ the vector representation
A ≡ the axial representation


IR Selection Rules
IRAgAuBgBu
Agxx
Auxx
Bgxx
Buxx

[ Note: x means allowed ]


Raman Selection Rules
RamanAgAuBgBu
Agxx
Auxx
Bgxx
Buxx

[ Note: x means allowed ]


Irreps Dimensions Irreps of the point group
Subduction of the rotation group D(L) to irreps of the group C2h(2/m)
L2L+1AgAuBgBu
011···
13·1·2
253·2·
37·3·4
495·4·
511·5·6
6137·6·
715·7·8
8179·8·
919·9·10
102111·10·



* 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