Curated collection
Finite symmetries in physics
Small nonabelian groups, discrete charges, rotational groups, binary lifts, and selected finite SU(3) subgroups. The representation summaries use ordinary complex irreps.
22 released records · classifications and individual objects are labeled separately.
| Object | Kind | Essential data | Coverage |
|---|---|---|---|
| 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 |