Conway groups

E29418

Conway groups are a set of three closely related sporadic simple groups discovered by John H. Conway in the study of symmetries of the Leech lattice in group theory.

AI illustration

How this image was made

AI-generated illustration of Conway groups

This AI-generated illustration was produced by black-forest-labs/FLUX.2-dev (1024x1024) from a prompt written by openai/gpt-oss-120b from the entity's label + description.

Prompt

Generate an image of Conway groups (Conway groups are a set of three closely related sporadic simple groups discovered by John H. Conway in the study of symmetries of the Leech lattice in group theory.)

All labels observed (8)

How this entity was disambiguated

Statements (48)

Predicate Object
instanceOf family of sporadic simple groups ⓘ
finite group ⓘ
finite simple group ⓘ
finite simple group ⓘ
finite simple group ⓘ
lattice in 24-dimensional Euclidean space ⓘ
mathematical concept ⓘ
mathematician ⓘ
sporadic simple group ⓘ
sporadic simple group ⓘ
sporadic simple group ⓘ
classification part of the 26 sporadic simple groups ⓘ
consistOf Co1 ⓘ
Co2 ⓘ
Co3 ⓘ
containsSubgroup Conway group Co1 ⓘ
linked to: Conway groups

Conway group Co2 ⓘ
linked to: Conway groups

Conway group Co3 ⓘ
linked to: Conway groups
definedOver finite sets ⓘ
dimension 24 ⓘ
discoveredBy John Horton Conway ⓘ
linked to: John H. Conway
discoveryContext study of symmetries of the Leech lattice ⓘ
field group theory ⓘ
group theory ⓘ
hasAutomorphismGroup automorphism group of the Leech lattice ⓘ
linked to: Conway groups
hasCardinality 3 ⓘ
hasMember Conway group Co1 ⓘ
linked to: Conway groups

Conway group Co2 ⓘ
linked to: Conway groups

Conway group Co3 ⓘ
linked to: Conway groups
hasProperty centerless ⓘ
finite simple groups ⓘ
non-abelian ⓘ
non-abelian ⓘ
non-abelian ⓘ
non-abelian simple groups ⓘ
isSubgroupOf automorphism group of the Leech lattice ⓘ
linked to: Conway groups

automorphism group of the Leech lattice ⓘ
linked to: Conway groups

automorphism group of the Leech lattice ⓘ
isSubsetOf sporadic simple groups ⓘ
knownFor discovery of Conway groups ⓘ
namedAfter John Horton Conway ⓘ
linked to: John H. Conway
order 4157776806543360000 ⓘ
42305421312000 ⓘ
495766656000 ⓘ
relatedTo Leech lattice ⓘ
Monster group ⓘ
automorphism group of the Leech lattice ⓘ
linked to: Conway groups
yearDiscoveredApprox 1960s ⓘ

How these facts were elicited

Referenced by (22)

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

John H. Conway → notableWork → Conway groups ⓘ
John Horton Conway → notableWork → Conway group ⓘ
subject linked to: Horton
linked to: Conway groups
Conway groups → relatedTo → automorphism group of the Leech lattice ⓘ
linked to: Conway groups
Conway groups → hasMember → Conway group Co1 ⓘ
linked to: Conway groups
Conway groups → hasMember → Conway group Co2 ⓘ
linked to: Conway groups
Conway groups → hasMember → Conway group Co3 ⓘ
linked to: Conway groups
Conway group Co1 → isSubgroupOf → automorphism group of the Leech lattice ⓘ
subject linked to: Conway groups
linked to: Conway groups
Conway group Co2 → isSubgroupOf → automorphism group of the Leech lattice ⓘ
subject linked to: Conway groups
linked to: Conway groups
automorphism group of the Leech lattice → containsSubgroup → Conway group Co1 ⓘ
subject linked to: Conway groups
linked to: Conway groups
automorphism group of the Leech lattice → containsSubgroup → Conway group Co2 ⓘ
subject linked to: Conway groups
linked to: Conway groups
automorphism group of the Leech lattice → containsSubgroup → Conway group Co3 ⓘ
subject linked to: Conway groups
linked to: Conway groups
Leech lattice → hasAutomorphismGroup → automorphism group of the Leech lattice ⓘ
subject linked to: Conway groups
linked to: Conway groups
John H. Conway → notableWork → Conway groups ⓘ
subject linked to: John
John H. Conway → hasConcept → Conway group ⓘ
subject linked to: John
linked to: Conway groups
Co1 → isSubgroupOf → Conway group Co0 ⓘ
linked to: Conway groups
Leech lattice → automorphismGroup → Conway group Co0 ⓘ
linked to: Conway groups
Leech lattice → automorphismGroup → Conway group Co1 ⓘ
linked to: Conway groups
Leech lattice → automorphismGroup → Conway group Co3 ⓘ
linked to: Conway groups
Leech lattice → relatedTo → Conway groups ⓘ
Monster group → hasSubgroup → Conway group Co1 ⓘ
linked to: Conway groups
M → containsSubgroup → Conway group Co_1 ⓘ
linked to: Conway groups