McL
E661158
McL is one of the 26 sporadic simple groups, known as the McLaughlin group, notable for its highly symmetric and exceptional finite group structure.
Statements (52)
| Predicate | Object |
|---|---|
| instanceOf |
finite simple group
ⓘ
group ⓘ sporadic simple group ⓘ |
| discoveredBy | Jack McLaughlin NERFINISHED ⓘ |
| fullName | McLaughlin group NERFINISHED ⓘ |
| hasElementOrder |
10
ⓘ
11 ⓘ 12 ⓘ 14 ⓘ 15 ⓘ 2 ⓘ 20 ⓘ 22 ⓘ 23 ⓘ 3 ⓘ 4 ⓘ 5 ⓘ 6 ⓘ 7 ⓘ 8 ⓘ 9 ⓘ |
| hasMaximalSubgroupIsomorphicTo |
2^4:A_7
ⓘ
2^6:U_4(2) ⓘ 2^{4+6}:3A_6 ⓘ 3^2:2S_5 ⓘ A_8 NERFINISHED ⓘ M_{22} NERFINISHED ⓘ M_{23} ⓘ U_4(3) ⓘ |
| hasNontrivialSchurMultiplier | true ⓘ |
| hasOuterAutomorphisms | true ⓘ |
| hasTransitiveActionOn | 275 points ⓘ |
| hasTrivialCenter | true ⓘ |
| isNonAbelian | true ⓘ |
| isPerfect | true ⓘ |
| isSimple | true ⓘ |
| isSubgroupOf |
Co_1
NERFINISHED
ⓘ
Monster group NERFINISHED ⓘ |
| minimalFaithfulPermutationDegree | 275 ⓘ |
| namedAfter | Jack McLaughlin NERFINISHED ⓘ |
| order | 898128000 ⓘ |
| orderFactorization |
11
ⓘ
23 ⓘ 2^7 ⓘ 3^6 ⓘ 5^3 ⓘ 7 ⓘ |
| outerAutomorphismGroupOrder | 2 ⓘ |
| rank3PermutationGroup | true ⓘ |
| relatedTo | Leech lattice NERFINISHED ⓘ |
| schurMultiplierOrder | 3 ⓘ |
| yearDiscovered | 1969 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.