database
GroupNames: D₈
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 |
|---|---|---|
| D₈ | Definition | Heading; Aliases; Generators and relations |
| D₈ | Order | Heading: order |
| D₈ | Center | Centre |
| D₈ | Abelian | Group-property labels; Commutator |
| D₈ | Simple finite group | Chief series and normal subgroups |
| D₈ | Ordinary complex irrep dimensions | Character table: identity column and orthogonal/complex/symplectic types |
| D₈ | Representations | Character table; matrix and permutation representations |
| D₈ | In physics | Character table; matrix and permutation representations |
| D₈ | Related group | Heading; Aliases; Generators and relations |
| D₈ | Related group | Heading; Aliases; Generators and relations |
| D₈ | Dihedral family; order eight | Aliases |
| D₈ · 1 | Definition | Ordinary character table of D₈; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · 1 | Complex dimension | Ordinary character table of D₈; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · 1 | Coefficient field | Ordinary character table of D₈; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · 1 | Frobenius–Schur type | Ordinary character table of D₈; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · 1 | Frobenius–Schur indicator | Ordinary character table of D₈; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · 1 | Complex conjugate irrep | Ordinary character table of D₈; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · 1 | Character and identity | Ordinary character table of D₈; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · 1 | Conventions and realization | Ordinary character table of D₈; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · 1 | Representation domain | Ordinary character table of D₈; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · a | Definition | Ordinary character table of D₈; the irrep a is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · a | Complex dimension | Ordinary character table of D₈; the irrep a is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · a | Coefficient field | Ordinary character table of D₈; the irrep a is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · a | Frobenius–Schur type | Ordinary character table of D₈; the irrep a is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · a | Frobenius–Schur indicator | Ordinary character table of D₈; the irrep a is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · a | Complex conjugate irrep | Ordinary character table of D₈; the irrep a is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · a | Character and identity | Ordinary character table of D₈; the irrep a is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · a | Conventions and realization | Ordinary character table of D₈; the irrep a is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · a | Representation domain | Ordinary character table of D₈; the irrep a is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · b | Definition | Ordinary character table of D₈; the irrep b is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · b | Complex dimension | Ordinary character table of D₈; the irrep b is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · b | Coefficient field | Ordinary character table of D₈; the irrep b is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · b | Frobenius–Schur type | Ordinary character table of D₈; the irrep b is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · b | Frobenius–Schur indicator | Ordinary character table of D₈; the irrep b is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · b | Complex conjugate irrep | Ordinary character table of D₈; the irrep b is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · b | Character and identity | Ordinary character table of D₈; the irrep b is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · b | Conventions and realization | Ordinary character table of D₈; the irrep b is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · b | Representation domain | Ordinary character table of D₈; the irrep b is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · c | Definition | Ordinary character table of D₈; the irrep c is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · c | Complex dimension | Ordinary character table of D₈; the irrep c is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · c | Coefficient field | Ordinary character table of D₈; the irrep c is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · c | Frobenius–Schur type | Ordinary character table of D₈; the irrep c is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · c | Frobenius–Schur indicator | Ordinary character table of D₈; the irrep c is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · c | Complex conjugate irrep | Ordinary character table of D₈; the irrep c is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · c | Character and identity | Ordinary character table of D₈; the irrep c is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · c | Conventions and realization | Ordinary character table of D₈; the irrep c is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · c | Representation domain | Ordinary character table of D₈; the irrep c is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · 2 | Definition | Ordinary character table of D₈; the irrep 2 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · 2 | Complex dimension | Ordinary character table of D₈; the irrep 2 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · 2 | Coefficient field | Ordinary character table of D₈; the irrep 2 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · 2 | Frobenius–Schur type | Ordinary character table of D₈; the irrep 2 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · 2 | Frobenius–Schur indicator | Ordinary character table of D₈; the irrep 2 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · 2 | Complex conjugate irrep | Ordinary character table of D₈; the irrep 2 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · 2 | Character and identity | Ordinary character table of D₈; the irrep 2 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · 2 | Conventions and realization | Ordinary character table of D₈; the irrep 2 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| D₈ · 2 | Representation domain | Ordinary character table of D₈; the irrep 2 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |