The mathematical reference

Family records.

Find the exact group, algebra, real form, family, or map. Follow its sources and supported calculations.

49finite group records41Lie group records38Lie algebras22specified maps

33 released records. Individual groups and parameterized families are counted separately.

Mathematical records
Object	Kind	Essential data	Coverage
$\mathrm{C}_{p}$ Cyclic groups of prime order	Family Finite	Parameterized family	classification Sourced record
$\mathrm{A}_{n}$ Simple alternating groups	Family Finite	Parameterized family	classification Sourced record
$\mathrm{PSL}(n,q)$ Projective special linear finite simple groups	Family Finite	Parameterized family	classification Sourced record
$\mathrm{PSU}(n,q)$ Projective special unitary finite simple groups	Family Finite	Parameterized family	classification Sourced record
$\mathrm{PSp}(2n,q)$ Projective symplectic finite simple groups	Family Finite	Parameterized family	classification Sourced record
$\mathrm P\Omega(2n+1,q)$ Odd-dimensional orthogonal finite simple groups	Family Finite	Parameterized family	classification Sourced record
$\mathrm P\Omega^{+}(2n,q)$ Plus-type even orthogonal finite simple groups	Family Finite	Parameterized family	classification Sourced record
$\mathrm P\Omega^{-}(2n,q)$ Minus-type even orthogonal finite simple groups	Family Finite	Parameterized family	classification Sourced record
$G_{2}(q)$ Finite simple groups of type G₂	Family Finite	Parameterized family	classification Sourced record
$F_{4}(q)$ Finite simple groups of type F₄	Family Finite	Parameterized family	classification Sourced record
$E_{6}(q)$ Finite simple groups of type E₆	Family Finite	Parameterized family	classification Sourced record
$E_{7}(q)$ Finite simple groups of type E₇	Family Finite	Parameterized family	classification Sourced record
$E_{8}(q)$ Finite simple groups of type E₈	Family Finite	Parameterized family	classification Sourced record
${}^{2}\!E_{6}(q)$ Finite simple groups of type ²E₆	Family Finite	Parameterized family	classification Sourced record
${}^{3}\!D_{4}(q)$ Finite simple groups of type ³D₄	Family Finite	Parameterized family	classification Sourced record
${}^{2}\!B_{2}(q)$ Suzuki simple groups	Family Finite	Parameterized family	classification Sourced record
${}^{2}\!G_{2}(q)$ Small Ree simple groups	Family Finite	Parameterized family	classification Sourced record
${}^{2}\!F_{4}(q)$ 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
$\mathrm{C}_{n}$ Finite cyclic groups	Family Finite	Parameterized family	reference Sourced record
$\mathrm{D}_{2n}$ Finite dihedral groups	Family Finite	Parameterized family	reference Sourced record
$\mathrm{Dic}_{n}$ Dicyclic groups	Family Finite	Parameterized family	reference Sourced record
$2T,\quad 2O,\quad 2I$ Exceptional binary polyhedral groups	Family Finite	Parameterized family	reference Sourced record
$\mathrm{S}_{n}$ Finite symmetric groups	Family Finite	Parameterized family	reference Sourced record
$\mathrm{A}_{r}$ Simple Lie type Aᵣ	Family Lie theory	Parameterized family	classification Sourced record
$\mathrm{B}_{r}$ Simple Lie type Bᵣ	Family Lie theory	Parameterized family	classification Sourced record
$\mathrm{C}_{r}$ Simple Lie type Cᵣ	Family Lie theory	Parameterized family	classification Sourced record
$\mathrm{D}_{r}$ Simple Lie type Dᵣ	Family Lie theory	Parameterized family	classification Sourced record
$\mathrm{E}_{6}$ Simple Lie type E₆	Family Lie theory	Parameterized family	classification Sourced record
$\mathrm{E}_{7}$ Simple Lie type E₇	Family Lie theory	Parameterized family	classification Sourced record
$\mathrm{E}_{8}$ Simple Lie type E₈	Family Lie theory	Parameterized family	classification Sourced record
$\mathrm{F}_{4}$ Simple Lie type F₄	Family Lie theory	Parameterized family	classification Sourced record
$\mathrm{G}_{2}$ 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.

Finite-simple classification Lie classification