database
GroupNames: S₃
Tim Dokchitser
Use in this reference: Linked source with original summaries of mathematical facts. Consult the source for its own terms; no blanket redistribution license is asserted.
Relevant material: Order, Centre, Aliases, generators and relations, Character table
Dependent assertions
| Record | Assertion | Source locator |
|---|---|---|
| S₃ | Definition | Heading; Aliases; Generators and relations |
| S₃ | Order | Heading: order |
| S₃ | Center | Centre |
| S₃ | Abelian | Group-property labels; Commutator |
| S₃ | Simple finite group | Chief series and normal subgroups |
| S₃ | Ordinary complex irrep dimensions | Character table: identity column and orthogonal/complex/symplectic types |
| S₃ | Representations | Character table; matrix and permutation representations |
| S₃ | In physics | Character table; matrix and permutation representations |
| S₃ | Related group | Heading; Aliases; Generators and relations |
| S₃ | Related group | Heading; Aliases; Generators and relations |
| S₃ | Symmetric family | Heading; Aliases; Generators and relations |
| S₃ | D₆ in the order-six convention | Aliases |
| S₃ · 1 | Definition | Ordinary character table of S₃; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₃ · 1 | Complex dimension | Ordinary character table of S₃; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₃ · 1 | Coefficient field | Ordinary character table of S₃; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₃ · 1 | Frobenius–Schur type | Ordinary character table of S₃; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₃ · 1 | Frobenius–Schur indicator | Ordinary character table of S₃; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₃ · 1 | Complex conjugate irrep | Ordinary character table of S₃; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₃ · 1 | Character and identity | Ordinary character table of S₃; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₃ · 1 | Conventions and realization | Ordinary character table of S₃; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₃ · 1 | Representation domain | Ordinary character table of S₃; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₃ · sgn | Definition | Ordinary character table of S₃; the irrep sgn is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₃ · sgn | Complex dimension | Ordinary character table of S₃; the irrep sgn is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₃ · sgn | Coefficient field | Ordinary character table of S₃; the irrep sgn is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₃ · sgn | Frobenius–Schur type | Ordinary character table of S₃; the irrep sgn is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₃ · sgn | Frobenius–Schur indicator | Ordinary character table of S₃; the irrep sgn is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₃ · sgn | Complex conjugate irrep | Ordinary character table of S₃; the irrep sgn is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₃ · sgn | Character and identity | Ordinary character table of S₃; the irrep sgn is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₃ · sgn | Conventions and realization | Ordinary character table of S₃; the irrep sgn is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₃ · sgn | Representation domain | Ordinary character table of S₃; the irrep sgn is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₃ · 2 | Definition | Ordinary character table of S₃; the irrep 2 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₃ · 2 | Complex dimension | Ordinary character table of S₃; the irrep 2 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₃ · 2 | Coefficient field | Ordinary character table of S₃; the irrep 2 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₃ · 2 | Frobenius–Schur type | Ordinary character table of S₃; the irrep 2 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₃ · 2 | Frobenius–Schur indicator | Ordinary character table of S₃; the irrep 2 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₃ · 2 | Complex conjugate irrep | Ordinary character table of S₃; the irrep 2 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₃ · 2 | Character and identity | Ordinary character table of S₃; the irrep 2 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₃ · 2 | Conventions and realization | Ordinary character table of S₃; the irrep 2 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₃ · 2 | Representation domain | Ordinary character table of S₃; the irrep 2 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |