database
GroupNames · A₄
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 |
|---|---|---|
| A₄ | Definition | Heading; Aliases; Generators and relations |
| A₄ | Order | Heading: order |
| A₄ | Center | Centre |
| A₄ | Abelian | Group-property labels; Commutator |
| A₄ | Simple finite group | Chief series and normal subgroups |
| A₄ | Ordinary complex irrep dimensions | Character table: identity column and orthogonal/complex/symplectic types |
| A₄ | Representations | Character table; matrix and permutation representations |
| A₄ | Related group | Heading; Aliases; Generators and relations |
| A₄ | Related group | Heading; Aliases; Generators and relations |
| A₄ | Related group | Heading; Aliases; Generators and relations |
| A₄ · 1 | Definition | Ordinary character table of A₄; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 1 | Complex dimension | Ordinary character table of A₄; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 1 | Coefficient field | Ordinary character table of A₄; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 1 | Frobenius–Schur type | Ordinary character table of A₄; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 1 | Frobenius–Schur indicator | Ordinary character table of A₄; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 1 | Complex conjugate irrep | Ordinary character table of A₄; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 1 | Character and identity | Ordinary character table of A₄; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 1 | Conventions and realization | Ordinary character table of A₄; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 1 | Representation domain | Ordinary character table of A₄; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 1′ | Definition | Ordinary character table of A₄; the irrep 1′ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 1′ | Complex dimension | Ordinary character table of A₄; the irrep 1′ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 1′ | Coefficient field | Ordinary character table of A₄; the irrep 1′ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 1′ | Frobenius–Schur type | Ordinary character table of A₄; the irrep 1′ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 1′ | Frobenius–Schur indicator | Ordinary character table of A₄; the irrep 1′ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 1′ | Complex conjugate irrep | Ordinary character table of A₄; the irrep 1′ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 1′ | Character and identity | Ordinary character table of A₄; the irrep 1′ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 1′ | Conventions and realization | Ordinary character table of A₄; the irrep 1′ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 1′ | Representation domain | Ordinary character table of A₄; the irrep 1′ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 1′ | Complex conjugate representation | Ordinary character table of A₄; the irrep 1′ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 1″ | Definition | Ordinary character table of A₄; the irrep 1″ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 1″ | Complex dimension | Ordinary character table of A₄; the irrep 1″ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 1″ | Coefficient field | Ordinary character table of A₄; the irrep 1″ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 1″ | Frobenius–Schur type | Ordinary character table of A₄; the irrep 1″ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 1″ | Frobenius–Schur indicator | Ordinary character table of A₄; the irrep 1″ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 1″ | Complex conjugate irrep | Ordinary character table of A₄; the irrep 1″ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 1″ | Character and identity | Ordinary character table of A₄; the irrep 1″ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 1″ | Conventions and realization | Ordinary character table of A₄; the irrep 1″ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 1″ | Representation domain | Ordinary character table of A₄; the irrep 1″ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 1″ | Complex conjugate representation | Ordinary character table of A₄; the irrep 1″ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 3 | Definition | Ordinary character table of A₄; the irrep 3 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 3 | Complex dimension | Ordinary character table of A₄; the irrep 3 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 3 | Coefficient field | Ordinary character table of A₄; the irrep 3 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 3 | Frobenius–Schur type | Ordinary character table of A₄; the irrep 3 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 3 | Frobenius–Schur indicator | Ordinary character table of A₄; the irrep 3 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 3 | Complex conjugate irrep | Ordinary character table of A₄; the irrep 3 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 3 | Character and identity | Ordinary character table of A₄; the irrep 3 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 3 | Conventions and realization | Ordinary character table of A₄; the irrep 3 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₄ · 3 | Representation domain | Ordinary character table of A₄; the irrep 3 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |