Classification Procedure for Point Groups

C = rotation axis           S = improper axis           i = inversion center           σ = plane of symmetry

Step #1
Examine for special groups.

  1. linear, no σ perpendicular to molecular axis - C∞v
  2. linear, σ perpendicular to molecular axis - D∞h
  3. tetrahedral - Td
  4. octahedral - Oh
  5. dodecahedral or icosahedral - Ih


Step #2
Examine for a Cn axis

Cn PresentCn Absent
Find Cn of highest n or unique n
(This axis is taken to be vertical by convention.)
σ present - Cs
i present - Ci
no symmetry elements other than E - C1


Step #3
Examine for S2n colinear with Cn

S2n PresentS2n Absent
No other symmetry elements present except i - S2n
Other symmetry elements present (Go to Step 4)
(Go to Step 4)


Step #4
Examine for n horizontal C2 axes
(where n is the order of highest order axis)

n C2 Axes Presentn C2 Axes Absent
Horizontal plane (σh) present - Dnh Horizontal plane (σh) present - Cnh
n Vertical planes (dihedral planes, σd, bisecting angles between C2 axes):
  • Present - Dnd
  • Absent - Dn
n Vertical planes (σv):
  • Present - Cnv
  • Absent - Cn