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.

All labels observed (1)

Label Occurrences
Held group canonical 1

How this entity was disambiguated

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 ⓘ
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 ⓘ
numberOfSporadicGroups 26 ⓘ
order 4030387200 ⓘ
orderFactorization 2^10 · 3^3 · 5^2 · 7^3 · 17 ⓘ
outerAutomorphismGroupOrder 2 ⓘ
yearOfDiscovery 1968 ⓘ

How these facts were elicited

Referenced by (1)

Full triples — surface form annotated when it differs from this entity's canonical label.

Monster group → hasSubgroup → Held group ⓘ