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Group records.
Find the exact group, algebra, real form, family, or map. Follow its sources and supported calculations.
49finite group records41Lie group records38Lie algebras22specified maps
90 released records. Individual groups and parameterized families are counted separately.
| Object | Kind | Essential data | Coverage |
|---|---|---|---|
| SU(2) Special unitary group | Group Lie theory | dimℝ 3 | executable 7 linked workbenchs |
| SO(3) Rotation group in three dimensions | Group Lie theory | dimℝ 3 | executable 2 linked workbenchs |
| SU(3) Special unitary group | Group Lie theory | dimℝ 8 | executable 8 linked workbenchs |
| PSU(3) Projective special unitary group | Group Lie theory | dimℝ 8 | executable 1 linked workbench |
| U(1) Circle group | Group Lie theory | dimℝ 1 | reference Sourced record |
| Spin(4) Euclidean spin group in four dimensions | Group Lie theory | dimℝ 6 | reference Sourced record |
| SL(2,ℂ) Lorentz spin group | Group Lie theory | dimℝ 6 | reference Sourced record |
| C₃ Cyclic group of order three | Group Finite | order 3 | executable 1 linked workbench |
| S₃ Symmetric group on three letters | Group Finite | order 6 | executable 1 linked workbench |
| A₄ Alternating group on four letters | Group Finite | order 12 | executable 2 linked workbenchs |
| S₄ Symmetric group on four letters | Group Finite | order 24 | executable 1 linked workbench |
| A₅ Alternating group on five letters | Group Finite | order 60 | executable 1 linked workbench |
| Q₈ Quaternion group | Group Finite | order 8 | executable 1 linked workbench |
| D₈ Dihedral group of order eight | Group Finite | order 8 | executable 1 linked workbench |
| C2 Cyclic group of order 2 | Group Finite | order 2 | reference Sourced record |
| C4 Cyclic group of order 4 | Group Finite | order 4 | reference Sourced record |
| C5 Cyclic group of order 5 | Group Finite | order 5 | reference Sourced record |
| C6 Cyclic group of order 6 | Group Finite | order 6 | reference Sourced record |
| V₄ Klein four-group | Group Finite | order 4 | reference Sourced record |
| D₁₀ Dihedral group of order ten | Group Finite | order 10 | reference Sourced record |
| D₁₂ Dihedral group of order twelve | Group Finite | order 12 | reference Sourced record |
| Dic₃ Dicyclic group of order twelve | Group Finite | order 12 | reference Sourced record |
| Q₁₆ Generalized quaternion group of order sixteen | Group Finite | order 16 | reference Sourced record |
| 2T Binary tetrahedral group | Group Finite | order 24 | reference Sourced record |
| 2O Binary octahedral group | Group Finite | order 48 | reference Sourced record |
| 2I Binary icosahedral group | Group Finite | order 120 | reference Sourced record |
| PSL(2,7) Projective special linear group PSL(2,7) | Group Finite | order 168 | reference Sourced record |
| Δ(27) Delta(27), the finite Heisenberg group | Group Finite | order 27 | reference Sourced record |
| A₆ Alternating group on six letters | Group Finite | order 360 | reference Sourced record |
| M₁₁ Mathieu group M11 | Group Finite | order 7920 | classification Sourced record |
| M₁₂ Mathieu group M12 | Group Finite | order 95040 | classification Sourced record |
| M₂₂ Mathieu group M22 | Group Finite | order 443520 | classification Sourced record |
| M₂₃ Mathieu group M23 | Group Finite | order 10200960 | classification Sourced record |
| M₂₄ Mathieu group M24 | Group Finite | order 244823040 | classification Sourced record |
| J₁ First Janko group | Group Finite | order 175560 | classification Sourced record |
| J₂ Hall–Janko group | Group Finite | order 604800 | classification Sourced record |
| J₃ Third Janko group | Group Finite | order 50232960 | classification Sourced record |
| J₄ Fourth Janko group | Group Finite | order 86775571046077562880 | classification Sourced record |
| Co₁ First Conway group | Group Finite | order 4157776806543360000 | classification Sourced record |
| Co₂ Second Conway group | Group Finite | order 42305421312000 | classification Sourced record |
| Co₃ Third Conway group | Group Finite | order 495766656000 | classification Sourced record |
| Fi₂₂ Fischer group Fi22 | Group Finite | order 64561751654400 | classification Sourced record |
| Fi₂₃ Fischer group Fi23 | Group Finite | order 4089470473293004800 | classification Sourced record |
| Fi₂₄′ Fischer simple group Fi24 prime | Group Finite | order 1255205709190661721292800 | classification Sourced record |
| HS Higman–Sims group | Group Finite | order 44352000 | classification Sourced record |
| McL McLaughlin group | Group Finite | order 898128000 | classification Sourced record |
| He Held group | Group Finite | order 4030387200 | classification Sourced record |
| Ru Rudvalis group | Group Finite | order 145926144000 | classification Sourced record |
| Suz Sporadic Suzuki group | Group Finite | order 448345497600 | classification Sourced record |
| O’N O’Nan group | Group Finite | order 460815505920 | classification Sourced record |
| HN Harada–Norton group | Group Finite | order 273030912000000 | classification Sourced record |
| Ly Lyons group | Group Finite | order 51765179004000000 | classification Sourced record |
| Th Thompson group | Group Finite | order 90745943887872000 | classification Sourced record |
| B Baby Monster group | Group Finite | order 4154781481226426191177580544000000 | classification Sourced record |
| M Monster group | Group Finite | order 808017424794512875886459904961710757005754368000000000 | classification Sourced record |
| ²F₄(2)′ Tits group | Group Finite | order 17971200 | classification Sourced record |
| SU(4) Special unitary group in four dimensions | Group Lie theory | dimℝ 15 | executable 4 linked workbenchs |
| PSU(4) Adjoint compact group of type A₃ | Group Lie theory | dimℝ 15 | reference Sourced record |
| SU(5) Special unitary group in five dimensions | Group Lie theory | dimℝ 24 | executable 4 linked workbenchs |
| U(2) Unitary group in two dimensions | Group Lie theory | dimℝ 4 | reference Sourced record |
| SO(4) Rotation group in four dimensions | Group Lie theory | dimℝ 6 | reference Sourced record |
| SO(5) Rotation group in five dimensions | Group Lie theory | dimℝ 10 | reference Sourced record |
| SO(6) Rotation group in six dimensions | Group Lie theory | dimℝ 15 | reference Sourced record |
| Sp(2) Compact symplectic group of quaternionic rank two | Group Lie theory | dimℝ 10 | executable 1 linked workbench |
| Sp(3) Compact symplectic group of quaternionic rank three | Group Lie theory | dimℝ 21 | reference Sourced record |
| Spin(8) Simply connected compact spin group in eight dimensions | Group Lie theory | dimℝ 28 | executable 1 linked workbench |
| SO(8) Rotation group in eight dimensions | Group Lie theory | dimℝ 28 | reference Sourced record |
| PSO(8) Adjoint compact group of type D₄ | Group Lie theory | dimℝ 28 | reference Sourced record |
| Spin(10) Simply connected compact spin group in ten dimensions | Group Lie theory | dimℝ 45 | executable 1 linked workbench |
| SO(10) Rotation group in ten dimensions | Group Lie theory | dimℝ 45 | reference Sourced record |
| G₂ compact Compact group of octonion automorphisms | Group Lie theory | dimℝ 14 | executable 1 linked workbench |
| F₄ compact Compact exceptional group of type F₄ | Group Lie theory | dimℝ 52 | executable 1 linked workbench |
| E₆ compact, simply connected Simply connected compact exceptional group of type E₆ | Group Lie theory | dimℝ 78 | executable 1 linked workbench |
| E₇ compact, simply connected Simply connected compact exceptional group of type E₇ | Group Lie theory | dimℝ 133 | executable 1 linked workbench |
| E₈ compact Compact exceptional group of type E₈ | Group Lie theory | dimℝ 248 | executable 1 linked workbench |
| E₆ compact, adjoint Adjoint compact exceptional group of type E₆ | Group Lie theory | dimℝ 78 | reference Sourced record |
| E₇ compact, adjoint Adjoint compact exceptional group of type E₇ | Group Lie theory | dimℝ 133 | reference Sourced record |
| SL(2, R) Real special linear group in two dimensions | Group Lie theory | dimℝ 3 | reference Sourced record |
| PSL(2, R) Adjoint real group of type A₁ | Group Lie theory | dimℝ 3 | reference Sourced record |
| Universal cover of SL(2, R) Simply connected group integrating sl(2,R) | Group Lie theory | dimℝ 3 | reference Sourced record |
| SL(3, R) Real special linear group in three dimensions | Group Lie theory | dimℝ 8 | reference Sourced record |
| SU(2,2) Indefinite special unitary group of signature (2,2) | Group Lie theory | dimℝ 15 | reference Sourced record |
| Sp(4, R) Real symplectic group on a four-dimensional space | Group Lie theory | dimℝ 10 | reference Sourced record |
| SO₀(1,3) Proper orthochronous Lorentz group in four dimensions | Group Lie theory | dimℝ 6 | reference Sourced record |
| SO₀(2,4) Identity component of the orthogonal group of signature (2,4) | Group Lie theory | dimℝ 15 | reference Sourced record |
| SO₀(2,3) Identity component of the orthogonal group of signature (2,3) | Group Lie theory | dimℝ 10 | reference Sourced record |
| SU(3) × SU(2) × U(1) Standard Model compact covering product | Group Lie theory | dimℝ 12 | executable 3 linked workbenchs |
| G_SM^(2) Standard Model global group with diagonal Z2 quotient | Group Lie theory | dimℝ 12 | executable 3 linked workbenchs |
| G_SM^(3) Standard Model global group with diagonal Z3 quotient | Group Lie theory | dimℝ 12 | executable 3 linked workbenchs |
| G_SM^(6) Standard Model global group with diagonal Z6 quotient | Group Lie theory | dimℝ 12 | executable 3 linked workbenchs |
Coverage is specific. Classification identifies a mathematical object or family. Reference supplies stated properties. Executable links to a bounded calculation. Read the coverage policy.