database
GroupNames: A₅
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 |
|---|---|---|
| A₅ | Definition | Heading; Aliases; Generators and relations |
| A₅ | Order | Heading: order |
| A₅ | Center | Centre |
| A₅ | Abelian | Group-property labels; Commutator |
| A₅ | Simple finite group | Simple label |
| A₅ | Ordinary complex irrep dimensions | Character table: identity column and orthogonal/complex/symplectic types |
| A₅ | Representations | Character table; matrix and permutation representations |
| A₅ | In physics | Character table; matrix and permutation representations |
| A₅ | Related group | Heading; Aliases; Generators and relations |
| A₅ | Related group | Heading; Aliases; Generators and relations |
| A₅ | Alternating simple family | Heading; Aliases; Generators and relations |
| A₅ | PSL(2,4) ≅ PSL(2,5) | Aliases |
| A₅ · 1 | Definition | Ordinary character table of A₅; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 1 | Complex dimension | Ordinary character table of A₅; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 1 | Coefficient field | Ordinary character table of A₅; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 1 | Frobenius–Schur type | Ordinary character table of A₅; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 1 | Frobenius–Schur indicator | Ordinary character table of A₅; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 1 | Complex conjugate irrep | Ordinary character table of A₅; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 1 | Character and identity | Ordinary character table of A₅; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 1 | Conventions and realization | Ordinary character table of A₅; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 1 | Representation domain | Ordinary character table of A₅; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 3 | Definition | Ordinary character table of A₅; the irrep 3 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 3 | Complex dimension | Ordinary character table of A₅; the irrep 3 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 3 | Coefficient field | Ordinary character table of A₅; the irrep 3 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 3 | Frobenius–Schur type | Ordinary character table of A₅; the irrep 3 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 3 | Frobenius–Schur indicator | Ordinary character table of A₅; the irrep 3 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 3 | Complex conjugate irrep | Ordinary character table of A₅; the irrep 3 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 3 | Character and identity | Ordinary character table of A₅; the irrep 3 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 3 | Conventions and realization | Ordinary character table of A₅; the irrep 3 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 3 | Representation domain | Ordinary character table of A₅; the irrep 3 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 3′ | Definition | Ordinary character table of A₅; the irrep 3′ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 3′ | Complex dimension | Ordinary character table of A₅; the irrep 3′ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 3′ | Coefficient field | Ordinary character table of A₅; the irrep 3′ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 3′ | Frobenius–Schur type | Ordinary character table of A₅; the irrep 3′ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 3′ | Frobenius–Schur indicator | Ordinary character table of A₅; the irrep 3′ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 3′ | Complex conjugate irrep | Ordinary character table of A₅; the irrep 3′ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 3′ | Character and identity | Ordinary character table of A₅; the irrep 3′ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 3′ | Conventions and realization | Ordinary character table of A₅; the irrep 3′ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 3′ | Representation domain | Ordinary character table of A₅; the irrep 3′ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 4 | Definition | Ordinary character table of A₅; the irrep 4 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 4 | Complex dimension | Ordinary character table of A₅; the irrep 4 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 4 | Coefficient field | Ordinary character table of A₅; the irrep 4 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 4 | Frobenius–Schur type | Ordinary character table of A₅; the irrep 4 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 4 | Frobenius–Schur indicator | Ordinary character table of A₅; the irrep 4 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 4 | Complex conjugate irrep | Ordinary character table of A₅; the irrep 4 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 4 | Character and identity | Ordinary character table of A₅; the irrep 4 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 4 | Conventions and realization | Ordinary character table of A₅; the irrep 4 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 4 | Representation domain | Ordinary character table of A₅; the irrep 4 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 5 | Definition | Ordinary character table of A₅; the irrep 5 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 5 | Complex dimension | Ordinary character table of A₅; the irrep 5 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 5 | Coefficient field | Ordinary character table of A₅; the irrep 5 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 5 | Frobenius–Schur type | Ordinary character table of A₅; the irrep 5 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 5 | Frobenius–Schur indicator | Ordinary character table of A₅; the irrep 5 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 5 | Complex conjugate irrep | Ordinary character table of A₅; the irrep 5 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 5 | Character and identity | Ordinary character table of A₅; the irrep 5 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 5 | Conventions and realization | Ordinary character table of A₅; the irrep 5 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| A₅ · 5 | Representation domain | Ordinary character table of A₅; the irrep 5 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |