Classification Procedure for Point Groups
C = rotation axis S = improper axis i = inversion center σ = plane of symmetry
Step #1
Examine for special groups.
- linear, no σ perpendicular to molecular axis - C∞v
- linear, σ perpendicular to molecular axis - D∞h
- tetrahedral - Td
- octahedral - Oh
- dodecahedral or icosahedral - Ih
Step #2
Examine for a Cn axis
| Cn Present | Cn 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 #2
Examine for S2n colinear with Cn
| S2n Present | S2n 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 Present | n C2 Axes Absent |
|---|---|
| Horizontal plane (σh) present - Dnh | Horizontal plane (σh) present - Cnh |
n Vertical planes (dihedral planes, σd, bisecting angles between C2 axes):
|
n Vertical planes (σv):
|