Symmetry Lab › Point groups

Point groups

32 point groups, 277 molecules, twelve families. Every card shows one molecule of the group with its symmetry elements drawn; open the card for the definition, the operations and the full list.

Linear?→High symmetry (T_d, O_h, I_h)?→Highest C_n→n C₂ ⊥ C_n? (D)→σ_h / σ_v / σ_d

Non-axial (C₁, Cᵢ, Cₛ) · 14 molecules

C_iorder 2 · 1 moleculeCHFCl–CHFCl (anti) — 1,2-Dichloro-1,2-difluoroethane, anti (meso)E, i

C_sorder 2 · 10 moleculesNOCl — Nitrosyl chlorideE, σ

C₁order 1 · 3 moleculesCHFClBr — BromochlorofluoromethaneE

Linear (C∞v, D∞h) · 31 molecules

C_∞vorder ∞ · 13 moleculesCO — Carbon monoxideE, 2C∞, ∞σᵥ

D_∞horder ∞ · 18 moleculesO₂ — DioxygenE, 2C∞, ∞σᵥ, i, 2S∞, ∞C₂

Cyclic (Cₙ) · 4 molecules

C₂order 2 · 4 moleculesH₂S₂ — Hydrogen disulfideE, C₂

Dihedral (Dₙ) · 5 molecules

D₂order 4 · 1 moleculeC₁₂H₁₀ — Biphenyl (twisted)E, C₂(z), C₂(y), C₂(x)

D₃order 6 · 2 molecules[Fe(C₂O₄)₃]³⁻ — Tris(oxalato)ferrate(III) (O atoms shown)E, 2C₃, 3C₂

D₅order 10 · 1 moleculeFe(C₅H₅)₂ (twisted) — Ferrocene, twisted by 18°E, 4C5, 5C₂ (rotations only)

D₆order 12 · 1 moleculeCr(C₆H₆)₂ (twisted) — Bis(benzene)chromium, twisted by 15°E, 5C6, 6C₂ (rotations only)

Pyramidal (Cₙᵥ) · 86 molecules

C_2vorder 4 · 43 moleculesSF₂ — Sulfur difluorideE, C₂, σᵥ(xz), σᵥ′(yz)

C_3vorder 6 · 30 moleculesPCl₃ — Phosphorus trichlorideE, 2C₃, 3σᵥ

C_4vorder 8 · 12 moleculesIF₅ — Iodine pentafluorideE, 2C₄, C₂, 2σᵥ, 2σd

C_5vorder 10 · 1 moleculeC₂₀H₁₀ — CorannuleneE, 2C₅, 2C₅², 5σᵥ

Reflection (Cₙₕ) · 9 molecules

C_2horder 4 · 7 moleculesN₂H₂ (trans) — trans-Diimide (diazene)E, C₂, i, σh

C_3horder 6 · 2 moleculesC₆H₃(OH)₃ — Phloroglucinol (benzene-1,3,5-triol)E, C₃, C₃², σh, S₃, S₃⁵

Prismatic (Dₙₕ) · 63 molecules

D_2horder 8 · 15 moleculesC₂H₄ — Ethylene (ethene)E, C₂(z), C₂(y), C₂(x), i, σ(xy), σ(xz), σ(yz)

D_3horder 12 · 22 moleculesBF₃ — Boron trifluorideE, 2C₃, 3C₂, σh, 2S₃, 3σᵥ

D_4horder 16 · 14 molecules[PtCl₄]²⁻ — Tetrachloroplatinate(II) ionE, 2C₄, C₂, 2C₂′, 2C₂″, i, 2S₄, σh, 2σᵥ, 2σd

D_5horder 20 · 5 moleculesIF₇ — Iodine heptafluorideE, 2C₅, 2C₅², 5C₂, σh, 2S₅, 2S₅³, 5σᵥ

D_6horder 24 · 4 moleculesC₆F₆ — HexafluorobenzeneE, 2C₆, 2C₃, C₂, 3C₂′, 3C₂″, i, 2S₃, 2S₆, σh, 3σd, 3σᵥ

D_7horder 28 · 1 moleculeC₇H₇⁺ — Tropylium ionE, 2C₇, 2C₇², 2C₇³, 7C₂, σh, 2S₇, 2S₇³, 2S₇⁵, 7σᵥ

D_8horder 32 · 2 moleculesU(C₈H₈)₂ — UranoceneE, 2C₈, 2C₈³, 2C₄, C₂, 4C₂′, 4C₂″, i, 2S₈, 2S₈³, 2S₄, σh, 4σᵥ, 4σd

Antiprismatic (Dₙd) · 15 molecules

D_2dorder 8 · 6 moleculesC₂H₄ (90° twisted) — Ethylene, perpendicular (rotation transition state)E, 2S₄, C₂, 2C₂′, 2σd

D_3dorder 12 · 4 moleculesC₂H₆ (staggered) — Ethane, staggeredE, 2C₃, 3C₂, i, 2S₆, 3σd

D_4dorder 16 · 3 molecules[Os₂Cl₈]²⁻ — Octachlorodiosmate(III) ionE, 2S₈, 2C₄, 2S₈³, C₂, 4C₂′, 4σd

D_5dorder 20 · 1 moleculeFe(C₅H₅)₂ (staggered) — Ferrocene, staggeredE, 2C₅, 2C₅², 5C₂, i, 2S₁₀³, 2S₁₀, 5σd

D_6dorder 24 · 1 moleculeCr(C₆H₆)₂ (staggered) — Bis(benzene)chromium, staggeredE, 2S₁₂, 2C₆, 2S₄, 2C₃, 2S₁₂⁵, C₂, 6C₂′, 6σd

Improper rotation (S₂ₙ) · 1 molecules

S₄order 4 · 1 moleculeC₈H₄(CH₃)₄ — 1,3,5,7-Tetramethylcyclo-octatetraene (methyl C shown)E, S₄, C₂, S₄³

Tetrahedral (T, Tₕ, Td) · 28 molecules

T_dorder 24 · 28 moleculesCH₄ — MethaneE, 8C₃, 3C₂, 6S₄, 6σd

Octahedral (O, Oₕ) · 18 molecules

O_horder 48 · 18 moleculesPF₆⁻ — Hexafluorophosphate ionE, 8C₃, 6C₂′, 6C₄, 3C₂, i, 6S₄, 8S₆, 3σh, 6σd

Icosahedral (I, Iₕ) · 3 molecules

I_horder 120 · 3 moleculesC₂₀H₂₀ — DodecahedraneE, 12C₅, 12C₅², 20C₃, 15C₂, i, 12S₁₀, 12S₁₀³, 20S₆, 15σ

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