Finite groups · Family
Finite simple groups of type G₂
q ≥ 3; the q = 2 parent group is not simple.
Classification coverageFinite simple classification
Parameter domain
q ≥ 3; the q = 2 parent group is not simple.
| Parameter | Allowed values |
|---|---|
| q | prime power q ≥ 3 |
Reference properties
Exceptions and identifications
q = 2: G₂(2)′ ≅ PSU(3,3), of index 2 in G₂(2). [sources]
Claims and sources
Each assertion has a stable identifier within this record and a source locator or derivation. Cite the dataset edition when referring to a corrected or historical claim.
Definition
The untwisted Chevalley group of type G₂ over Fq.
- Finite simple groups: Lecture 4 — Exceptional groupsG₂(q), order and simplicityOpen source
family:finite-g2#definitionParameter domain
q: prime power q ≥ 3
- Finite simple groups: Lecture 4 — Exceptional groupsG₂(q), order and simplicityOpen source
family:finite-g2#parametersScope and restrictions
q ≥ 3; the q = 2 parent group is not simple.
- Finite simple groups: Lecture 4 — Exceptional groupsG₂(q), order and simplicityOpen source
family:finite-g2#restrictionExceptions and identifications
q = 2: G₂(2)′ ≅ PSU(3,3), of index 2 in G₂(2).
- Groups with a p-element acting with a single non-trivial Jordan block on a simple module in characteristic pSection 7, seven exceptional isomorphisms before Proposition 24Open source
- Finite simple groups: Lecture 4 — Exceptional groupsG₂(q), small caseOpen source
family:finite-g2#exceptions-1