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49finite group records41Lie group records38Lie algebras22specified maps
33 released records. Individual groups and parameterized families are counted separately.
| Object | Kind | Essential data | Coverage |
|---|---|---|---|
| Cₚ Cyclic groups of prime order | Family Finite | Parameterized family | classification Sourced record |
| Aₙ Simple alternating groups | Family Finite | Parameterized family | classification Sourced record |
| PSL(n,q) Projective special linear finite simple groups | Family Finite | Parameterized family | classification Sourced record |
| PSU(n,q) Projective special unitary finite simple groups | Family Finite | Parameterized family | classification Sourced record |
| PSp(2n,q) Projective symplectic finite simple groups | Family Finite | Parameterized family | classification Sourced record |
| PΩ(2n+1,q) Odd-dimensional orthogonal finite simple groups | Family Finite | Parameterized family | classification Sourced record |
| PΩ⁺(2n,q) Plus-type even orthogonal finite simple groups | Family Finite | Parameterized family | classification Sourced record |
| PΩ⁻(2n,q) Minus-type even orthogonal finite simple groups | Family Finite | Parameterized family | classification Sourced record |
| G₂(q) Finite simple groups of type G₂ | Family Finite | Parameterized family | classification Sourced record |
| F₄(q) Finite simple groups of type F₄ | Family Finite | Parameterized family | classification Sourced record |
| E₆(q) Finite simple groups of type E₆ | Family Finite | Parameterized family | classification Sourced record |
| E₇(q) Finite simple groups of type E₇ | Family Finite | Parameterized family | classification Sourced record |
| E₈(q) Finite simple groups of type E₈ | Family Finite | Parameterized family | classification Sourced record |
| ²E₆(q) Finite simple groups of type ²E₆ | Family Finite | Parameterized family | classification Sourced record |
| ³D₄(q) Finite simple groups of type ³D₄ | Family Finite | Parameterized family | classification Sourced record |
| ²B₂(q) Suzuki simple groups | Family Finite | Parameterized family | classification Sourced record |
| ²G₂(q) Small Ree simple groups | Family Finite | Parameterized family | classification Sourced record |
| ²F₄(q) Large Ree simple groups | Family Finite | Parameterized family | classification Sourced record |
| Sporadic The 26 sporadic finite simple groups | Family Finite | Parameterized family | classification Sourced record |
| Cₙ Finite cyclic groups | Family Finite | Parameterized family | reference Sourced record |
| D₂ₙ Finite dihedral groups | Family Finite | Parameterized family | reference Sourced record |
| Dicₙ Dicyclic groups | Family Finite | Parameterized family | reference Sourced record |
| 2T · 2O · 2I Exceptional binary polyhedral groups | Family Finite | Parameterized family | reference Sourced record |
| Sₙ Finite symmetric groups | Family Finite | Parameterized family | reference Sourced record |
| Aᵣ Simple Lie type Aᵣ | Family Lie theory | Parameterized family | classification Sourced record |
| Bᵣ Simple Lie type Bᵣ | Family Lie theory | Parameterized family | classification Sourced record |
| Cᵣ Simple Lie type Cᵣ | Family Lie theory | Parameterized family | classification Sourced record |
| Dᵣ Simple Lie type Dᵣ | Family Lie theory | Parameterized family | classification Sourced record |
| E₆ Simple Lie type E₆ | Family Lie theory | Parameterized family | classification Sourced record |
| E₇ Simple Lie type E₇ | Family Lie theory | Parameterized family | classification Sourced record |
| E₈ Simple Lie type E₈ | Family Lie theory | Parameterized family | classification Sourced record |
| F₄ Simple Lie type F₄ | Family Lie theory | Parameterized family | classification Sourced record |
| G₂ Simple Lie type G₂ | Family Lie theory | Parameterized family | classification Sourced record |
Coverage is specific. Classification identifies a mathematical object or family. Reference supplies stated properties. Executable links to a bounded calculation. Read the coverage policy.