Scheme 1.3 Flowchart for
assigning the group symmetry
([1], p. 10)
Table 1.4 Symmetry elements in some common point groups
Point
group
Symmetry elements
a
Examples
C 1
No symmetry
SiBrClFI
C 2
One C 2 axis
H 2 O 2
C nh
One n-fold axis and a horizontal plane r h which must be
perpendicular to the n-fold axis
trans-C 2 H 2 Cl 2
(C 2 h)
C 2v
One C 2 axis and two r v planes
H 2 O, SO 2 Cl 2 ,
SiCl 2 Br 2
C 3v
One C 3 axis and three r v planes
NH 3 , CH 3 Cl,
POCl 3
D 2h
Three C 2 axes all ⊥ , two r v planes, one r h
plane, and a center of symmetry
N 2 O 4 (planar)
D 3h
One C 3 , three C 2 axes ⊥ to C 3 , three r v planes, and one r h
BCl 3
D 2d
Three C 2 axes, two r d planes, and one S 4
(coincident with one C 2 )
H 2 C=C=CH 2
T d
Three C 2 axes ⊥ to each other, four C 3 , six r,
and three S 4 containing C 2
CH 4 , SiCl 4
a All point groups possess the identity element, E
1.5 Group Theory
11