McLaughlin group
E656679
The McLaughlin group is one of the 26 sporadic simple groups in finite group theory, notable for its rich symmetry properties and role in the classification of finite simple groups.
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
finite group
ⓘ
finite simple group ⓘ sporadic simple group ⓘ |
| actsOn | McLaughlin graph NERFINISHED ⓘ |
| actsTransitivelyOn | 275 points ⓘ |
| discoveredBy | Jack McLaughlin NERFINISHED ⓘ |
| discoveryYear | 1969 ⓘ |
| hasAbbreviation | McL NERFINISHED ⓘ |
| hasAtlasName | McL NERFINISHED ⓘ |
| hasAutomorphismGroup | McL:2 NERFINISHED ⓘ |
| hasMaximalSubgroup |
11:5
ⓘ
2^3+6:3^2:2 ⓘ 2^4:A7 NERFINISHED ⓘ 2^6:3·S6 NERFINISHED ⓘ 2·A8 ⓘ 3^1+4:2·S4 NERFINISHED ⓘ 3^2+4:2^2·S4 ⓘ 3^2:2S5 NERFINISHED ⓘ 3^4:2·S5 NERFINISHED ⓘ 5^1+2:4A4 NERFINISHED ⓘ 5^2:4S4 ⓘ 7:6 ⓘ A7 ⓘ L2(11) ⓘ M22 NERFINISHED ⓘ M22:2 NERFINISHED ⓘ U4(3) NERFINISHED ⓘ |
| hasMinimalFaithfulComplexRepresentationDegree |
22
ⓘ
77 ⓘ |
| hasMinimalFaithfulPermutationDegree | 275 ⓘ |
| hasOuterAutomorphismGroup | C2 ⓘ |
| hasPointStabilizer |
3^4:2·S5
NERFINISHED
ⓘ
U4(3) NERFINISHED ⓘ |
| hasRank3PermutationDegree | 275 ⓘ |
| hasRank3PermutationRepresentation | true ⓘ |
| hasRelatedGeometry | McLaughlin graph NERFINISHED ⓘ |
| hasSylow11SubgroupOrder | 11 ⓘ |
| hasSylow2SubgroupOrder | 128 ⓘ |
| hasSylow3SubgroupOrder | 729 ⓘ |
| hasSylow5SubgroupOrder | 125 ⓘ |
| hasSylow7SubgroupOrder | 7 ⓘ |
| hasTrivialCenter | true ⓘ |
| isInvolvedIn | classification of finite simple groups ⓘ |
| isOneOf | 26 sporadic simple groups ⓘ |
| isPerfectGroup | true ⓘ |
| order | 898128000 ⓘ |
| orderFactorization | 2^7 · 3^6 · 5^3 · 7 · 11 ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.