Examples of molecules and their point groups

Example 1 --- CO₂

• linear or low symmetry? Yes
• center of inversion? Yes
  
  D_∞h

Example 2 --- BF₃

• linear low symmetry? No
• C_n axis? Yes- Principal axis C₃ passing through B.
• nC₂ axes? Yes 3C₂ axes
• σ_h? Yes
  
  D_3h

Example 3 --- CCl₄

• highly symmetric? Yes
• Sure, C_n axis of C₃ or higher? Yes
• Any C₅ or C₄? No
• 3S₄? Yes. 4C₃ axes passing through C-Cl bond,3C₂ in each x,y,z dimensions. 6 σ_d mirror planes one for each Cl-C-Cl bond
  
  T_d

Example 4 --- 1,3,5,7 -tetrafluoracyclooctatetrane

• linear low symmetry? No
• highly symmetric? No
• C_n axis? No
• σ_h? No
• σ_v? No
  
  S₄

Example 5 --- SF₆

• highly symmetric? Yes
• Sure, C_n axis of C₃ or higher? Yes, 4C₃ and 3C₄
• inversion center? yes
  
  O_h

Example 6 --- BrF₅

• linear, low symmetry or high symmetry? No
• C_n axis perp to C₂? No
• σ_h? No
• σ_v? Yes
  
  C_4v

Example 7 --- [Co(en)₃]³⁺

• linear, low symmetry or high symmetry? No
• C_n axis? Yes- Principal axis C₃
• nC₂ axes perp to C₂? Yes
• σ_h? No
• σ_d? No
  
  D₃

Example 8 --- Naphthalene

• linear, low symmetry or high symmetry? No
• C_n axis? Yes- Principal axis C₂
• nC₂ axes perp to C₂? Yes
• σ_h? Yes
  
  D_2h