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.

Read the conventions and classification

22 released records · classifications and individual objects are labeled separately.

Finite symmetries in physics
Object	Kind	Essential data	Coverage
$\mathrm{C}_{3}$ Cyclic group of order three	Group Finite	order 3	executable 1 linked workbench
$\mathrm{S}_{3}$ Symmetric group on three letters	Group Finite	order 6	executable 1 linked workbench
$\mathrm{A}_{4}$ Alternating group on four letters	Group Finite	order 12	executable 2 linked workbenchs
$\mathrm{S}_{4}$ Symmetric group on four letters	Group Finite	order 24	executable 1 linked workbench
$\mathrm{A}_{5}$ Alternating group on five letters	Group Finite	order 60	executable 1 linked workbench
$\mathrm{Q}_{8}$ Quaternion group	Group Finite	order 8	executable 1 linked workbench
$\mathrm{D}_{8}$ Dihedral group of order eight	Group Finite	order 8	executable 1 linked workbench
$C_{2}$ Cyclic group of order 2	Group Finite	order 2	reference Sourced record
$C_{4}$ Cyclic group of order 4	Group Finite	order 4	reference Sourced record
$C_{5}$ Cyclic group of order 5	Group Finite	order 5	reference Sourced record
$C_{6}$ Cyclic group of order 6	Group Finite	order 6	reference Sourced record
$\mathrm{V}_{4}$ Klein four-group	Group Finite	order 4	reference Sourced record
$\mathrm{D}_{10}$ Dihedral group of order ten	Group Finite	order 10	reference Sourced record
$\mathrm{D}_{12}$ Dihedral group of order twelve	Group Finite	order 12	reference Sourced record
$\mathrm{Dic}_{3}$ Dicyclic group of order twelve	Group Finite	order 12	reference Sourced record
$\mathrm{Q}_{16}$ 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
$\mathrm{PSL}(2,7)$ Projective special linear group PSL(2,7)	Group Finite	order 168	reference Sourced record
$\Delta(27)$ Delta(27), the finite Heisenberg group	Group Finite	order 27	reference Sourced record
$\mathrm{A}_{6}$ Alternating group on six letters	Group Finite	order 360	reference Sourced record