Held group
E656678
The Held group is a sporadic simple group in the classification of finite simple groups, discovered by Dieter Held and notable for its highly symmetric and exceptional structure.
Statements (52)
| Predicate | Object |
|---|---|
| instanceOf |
finite simple group
ⓘ
group in abstract algebra ⓘ sporadic simple group ⓘ |
| actsOn | set of 2058 points ⓘ |
| alsoKnownAs | He ⓘ |
| belongsTo | sporadic groups ⓘ |
| classificationContext | classification of finite simple groups ⓘ |
| discoverer | Dieter Held NERFINISHED ⓘ |
| hasDoubleCover | 2.He ⓘ |
| hasElementOrder |
10
ⓘ
119 ⓘ 1190 ⓘ 12 ⓘ 14 ⓘ 15 ⓘ 17 ⓘ 170 ⓘ 1785 ⓘ 2 ⓘ 21 ⓘ 238 ⓘ 2380 ⓘ 28 ⓘ 3 ⓘ 30 ⓘ 357 ⓘ 3570 ⓘ 4 ⓘ 42 ⓘ 5 ⓘ 51 ⓘ 595 ⓘ 6 ⓘ 7 ⓘ 714 ⓘ 8 ⓘ 85 ⓘ |
| hasOuterAutomorphisms | true ⓘ |
| hasTripleCover | 3.He ⓘ |
| hasTrivialCenter | true ⓘ |
| isFinite | true ⓘ |
| isNonAbelian | true ⓘ |
| isSimple | true ⓘ |
| minimalFaithfulLinearRepresentationCharacteristic0 | 51 ⓘ |
| minimalFaithfulPermutationDegree | 2058 ⓘ |
| minimalFaithfulPermutationRepresentation | transitive of degree 2058 ⓘ |
| namedAfter | Dieter Held NERFINISHED ⓘ |
| numberOfSporadicGroups | 26 ⓘ |
| order | 4030387200 ⓘ |
| orderFactorization | 2^10 · 3^3 · 5^2 · 7^3 · 17 ⓘ |
| outerAutomorphismGroupOrder | 2 ⓘ |
| yearOfDiscovery | 1968 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.