Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Weyl_group
gptkb:group_of_people |
| gptkbp:automorphismGroup |
order 2
|
| gptkbp:centralTo |
cyclic of order gcd(3, q-1)
|
| gptkbp:definedIn |
finite field of order q
|
| gptkbp:Dynkin_diagram |
gptkb:E_6
|
| gptkbp:hasSubgroup |
gptkb:E_7(q)
gptkb:E_8(q) |
| gptkbp:hasTwistedForm |
gptkb:2E_6(q)
|
| https://www.w3.org/2000/01/rdf-schema#label |
E 6(q)
|
| gptkbp:isGroupOfLieType |
yes
|
| gptkbp:isPerfect |
yes
|
| gptkbp:isQuasisimple |
yes
|
| gptkbp:isSimple |
q > 1, q \\neq 2
q > 2 yes, except for small q |
| gptkbp:isSplitForm |
yes
|
| gptkbp:order |
q^{36} (q^{12}-1)(q^9-1)(q^8-1)(q^6-1)(q^5-1)(q^2-1)/gcd(3,q-1)
|
| gptkbp:rank |
6
|
| gptkbp:relatedTo |
gptkb:exceptional_groups_of_Lie_type
gptkb:E_6_Lie_type |
| gptkbp:bfsParent |
gptkb:G_2(q)
|
| gptkbp:bfsLayer |
7
|