database
GroupNames: S₄
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 |
|---|---|---|
| S₄ | Definition | Heading; Aliases; Generators and relations |
| S₄ | Order | Heading: order |
| S₄ | Center | Centre |
| S₄ | Abelian | Group-property labels; Commutator |
| S₄ | Simple finite group | Chief series and normal subgroups |
| S₄ | Ordinary complex irrep dimensions | Character table: identity column and orthogonal/complex/symplectic types |
| S₄ | Representations | Character table; matrix and permutation representations |
| S₄ | Related group | Heading; Aliases; Generators and relations |
| S₄ | Related group | Heading; Aliases; Generators and relations |
| S₄ | Related group | Heading; Aliases; Generators and relations |
| S₄ | Symmetric family | Heading; Aliases; Generators and relations |
| S₄ · 1 | Definition | Ordinary character table of S₄; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 1 | Complex dimension | Ordinary character table of S₄; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 1 | Coefficient field | Ordinary character table of S₄; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 1 | Frobenius–Schur type | Ordinary character table of S₄; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 1 | Frobenius–Schur indicator | Ordinary character table of S₄; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 1 | Complex conjugate irrep | Ordinary character table of S₄; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 1 | Character and identity | Ordinary character table of S₄; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 1 | Conventions and realization | Ordinary character table of S₄; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 1 | Representation domain | Ordinary character table of S₄; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · sgn | Definition | Ordinary character table of S₄; the irrep sgn is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · sgn | Complex dimension | Ordinary character table of S₄; the irrep sgn is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · sgn | Coefficient field | Ordinary character table of S₄; the irrep sgn is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · sgn | Frobenius–Schur type | Ordinary character table of S₄; the irrep sgn is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · sgn | Frobenius–Schur indicator | Ordinary character table of S₄; the irrep sgn is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · sgn | Complex conjugate irrep | Ordinary character table of S₄; the irrep sgn is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · sgn | Character and identity | Ordinary character table of S₄; the irrep sgn is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · sgn | Conventions and realization | Ordinary character table of S₄; the irrep sgn is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · sgn | Representation domain | Ordinary character table of S₄; the irrep sgn is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 2 | Definition | Ordinary character table of S₄; the irrep 2 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 2 | Complex dimension | Ordinary character table of S₄; the irrep 2 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 2 | Coefficient field | Ordinary character table of S₄; the irrep 2 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 2 | Frobenius–Schur type | Ordinary character table of S₄; the irrep 2 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 2 | Frobenius–Schur indicator | Ordinary character table of S₄; the irrep 2 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 2 | Complex conjugate irrep | Ordinary character table of S₄; the irrep 2 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 2 | Character and identity | Ordinary character table of S₄; the irrep 2 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 2 | Conventions and realization | Ordinary character table of S₄; the irrep 2 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 2 | Representation domain | Ordinary character table of S₄; the irrep 2 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 3 | Definition | Ordinary character table of S₄; the irrep 3 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 3 | Complex dimension | Ordinary character table of S₄; the irrep 3 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 3 | Coefficient field | Ordinary character table of S₄; the irrep 3 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 3 | Frobenius–Schur type | Ordinary character table of S₄; the irrep 3 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 3 | Frobenius–Schur indicator | Ordinary character table of S₄; the irrep 3 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 3 | Complex conjugate irrep | Ordinary character table of S₄; the irrep 3 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 3 | Character and identity | Ordinary character table of S₄; the irrep 3 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 3 | Conventions and realization | Ordinary character table of S₄; the irrep 3 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 3 | Representation domain | Ordinary character table of S₄; the irrep 3 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 3′ | Definition | Ordinary character table of S₄; the irrep 3′ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 3′ | Complex dimension | Ordinary character table of S₄; the irrep 3′ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 3′ | Coefficient field | Ordinary character table of S₄; the irrep 3′ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 3′ | Frobenius–Schur type | Ordinary character table of S₄; the irrep 3′ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 3′ | Frobenius–Schur indicator | Ordinary character table of S₄; the irrep 3′ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 3′ | Complex conjugate irrep | Ordinary character table of S₄; the irrep 3′ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 3′ | Character and identity | Ordinary character table of S₄; the irrep 3′ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 3′ | Conventions and realization | Ordinary character table of S₄; the irrep 3′ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| S₄ · 3′ | Representation domain | Ordinary character table of S₄; the irrep 3′ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |