database
GroupNames: C₃
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 |
|---|---|---|
| C₃ | Definition | Heading; Aliases; Generators and relations |
| C₃ | Order | Heading: order |
| C₃ | Center | Abelian label; upper central series |
| C₃ | Abelian | Group-property labels; Commutator |
| C₃ | Simple finite group | Simple label |
| C₃ | Ordinary complex irrep dimensions | Character table: identity column and orthogonal/complex/symplectic types |
| C₃ | Representations | Character table; matrix and permutation representations |
| C₃ | In physics | Character table; matrix and permutation representations |
| C₃ | Related group | Heading; Aliases; Generators and relations |
| C₃ | Related group | Heading; Aliases; Generators and relations |
| C₃ | Cyclic family | Heading; Aliases; Generators and relations |
| C₃ | Prime-order simple family | Simple label |
| C₃ · 1 | Definition | Ordinary character table of C₃; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| C₃ · 1 | Complex dimension | Ordinary character table of C₃; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| C₃ · 1 | Coefficient field | Ordinary character table of C₃; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| C₃ · 1 | Frobenius–Schur type | Ordinary character table of C₃; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| C₃ · 1 | Frobenius–Schur indicator | Ordinary character table of C₃; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| C₃ · 1 | Complex conjugate irrep | Ordinary character table of C₃; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| C₃ · 1 | Character and identity | Ordinary character table of C₃; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| C₃ · 1 | Conventions and realization | Ordinary character table of C₃; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| C₃ · 1 | Representation domain | Ordinary character table of C₃; the irrep 1 is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| C₃ · χ | Definition | Ordinary character table of C₃; the irrep χ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| C₃ · χ | Complex dimension | Ordinary character table of C₃; the irrep χ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| C₃ · χ | Coefficient field | Ordinary character table of C₃; the irrep χ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| C₃ · χ | Frobenius–Schur type | Ordinary character table of C₃; the irrep χ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| C₃ · χ | Frobenius–Schur indicator | Ordinary character table of C₃; the irrep χ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| C₃ · χ | Complex conjugate irrep | Ordinary character table of C₃; the irrep χ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| C₃ · χ | Character and identity | Ordinary character table of C₃; the irrep χ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| C₃ · χ | Conventions and realization | Ordinary character table of C₃; the irrep χ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| C₃ · χ | Representation domain | Ordinary character table of C₃; the irrep χ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| C₃ · χ | Complex conjugate representation | Ordinary character table of C₃; the irrep χ is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| C₃ · χ² | Definition | Ordinary character table of C₃; the irrep χ² is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| C₃ · χ² | Complex dimension | Ordinary character table of C₃; the irrep χ² is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| C₃ · χ² | Coefficient field | Ordinary character table of C₃; the irrep χ² is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| C₃ · χ² | Frobenius–Schur type | Ordinary character table of C₃; the irrep χ² is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| C₃ · χ² | Frobenius–Schur indicator | Ordinary character table of C₃; the irrep χ² is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| C₃ · χ² | Complex conjugate irrep | Ordinary character table of C₃; the irrep χ² is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| C₃ · χ² | Character and identity | Ordinary character table of C₃; the irrep χ² is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| C₃ · χ² | Conventions and realization | Ordinary character table of C₃; the irrep χ² is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| C₃ · χ² | Representation domain | Ordinary character table of C₃; the irrep χ² is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |
| C₃ · χ² | Complex conjugate representation | Ordinary character table of C₃; the irrep χ² is identified by the complete character vector in this record. Local class representatives and labels are supplied with the table. |