Co1

E169183

Co1 is the largest of the three sporadic Conway groups, a finite simple group arising as a symmetry group related to the Leech lattice in 24-dimensional space.

All labels observed (3)

Label Occurrences
Co1 canonical 2
Co1·2 1
Co_1 1

How this entity was disambiguated

Statements (53)

Predicate Object
instanceOf Conway group ⓘ
finite simple group ⓘ
sporadic simple group ⓘ
actsOn Leech lattice ⓘ
belongsTo 26 sporadic simple groups ⓘ
constructedAs quotient of Co0 by its center ⓘ
definedOver integers ⓘ
dimensionOfAssociatedLattice 24 ⓘ
discoverer John Horton Conway ⓘ
linked to: John H. Conway
hasAtlasName Co1 ⓘ
hasAutomorphismGroup Co1·2 ⓘ
linked to: Co1
hasConjugacyClasses 21 ⓘ
hasElementOfOrder 11 ⓘ
13 ⓘ
2 ⓘ
23 ⓘ
29 ⓘ
3 ⓘ
4 ⓘ
5 ⓘ
6 ⓘ
7 ⓘ
8 ⓘ
hasPrimeDivisor 11 ⓘ
13 ⓘ
2 ⓘ
23 ⓘ
29 ⓘ
3 ⓘ
5 ⓘ
7 ⓘ
hasRank3PermutationRepresentation true ⓘ
hasTrivialCenter true ⓘ
isInvolvedIn classification of finite simple groups ⓘ
isLargestOf three sporadic Conway groups ⓘ
isNonAbelian true ⓘ
isPerfectGroup true ⓘ
isSubgroupOf Conway group Co0 ⓘ
linked to: Conway groups
minimalFaithfulLinearRepresentationDegree 24 ⓘ
minimalFaithfulPermutationDegree 98280 ⓘ
order 4157776806543360000 ⓘ
orderFactorization 11 ⓘ
13 ⓘ
23 ⓘ
29 ⓘ
2^21 ⓘ
3^9 ⓘ
5^4 ⓘ
7^2 ⓘ
outerAutomorphismGroup C2 ⓘ
relatedGroup Co2 ⓘ
Co3 ⓘ
relatedTo Leech lattice ⓘ

How these facts were elicited

Referenced by (4)

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

Co1 → hasAutomorphismGroup → Co1·2 ⓘ
linked to: Co1
McL → isSubgroupOf → Co_1 ⓘ
linked to: Co1