M
E656673
M is the standard notation for the Monster group, the largest sporadic simple group in group theory and a central object in the study of finite simple groups and monstrous moonshine.
Statements (56)
| Predicate | Object |
|---|---|
| instanceOf |
Monster group
ⓘ
finite simple group ⓘ sporadic simple group ⓘ |
| actsOn | 196883-dimensional complex vector space ⓘ |
| alternativeName |
Fischer–Griess Monster
NERFINISHED
ⓘ
Friendly Giant NERFINISHED ⓘ Griess Monster NERFINISHED ⓘ Monster NERFINISHED ⓘ |
| constructedAs | automorphism group of a 196884-dimensional commutative nonassociative algebra ⓘ |
| constructedBy | Robert Griess NERFINISHED ⓘ |
| constructionYear | 1980 ⓘ |
| containsSubgroup |
Baby Monster group B
NERFINISHED
ⓘ
Conway group Co_1 NERFINISHED ⓘ Fischer group Fi_24' NERFINISHED ⓘ many other sporadic simple groups ⓘ |
| field |
finite group theory
ⓘ
group theory ⓘ |
| hasConjugacyClasses | 194 ⓘ |
| hasIrreducibleComplexCharacters | 194 ⓘ |
| hasNextComplexRepresentationDimension | 21296876 ⓘ |
| hasPrimeDivisor |
11
ⓘ
13 ⓘ 17 ⓘ 19 ⓘ 2 ⓘ 23 ⓘ 29 ⓘ 3 ⓘ 31 ⓘ 41 ⓘ 47 ⓘ 5 ⓘ 59 ⓘ 7 ⓘ 71 ⓘ |
| hasSchurMultiplierOrder | 1 ⓘ |
| hasSmallestNontrivialComplexRepresentationDimension | 196883 ⓘ |
| hasTrivialCenter | true ⓘ |
| hasTrivialOuterAutomorphismGroup | true ⓘ |
| isAutomorphismGroupOf |
Monster vertex operator algebra
NERFINISHED
ⓘ
moonshine module V^natural ⓘ |
| isCentralObjectIn |
classification of finite simple groups
ⓘ
monstrous moonshine conjectures NERFINISHED ⓘ |
| isLargestKnownFiniteSimpleGroup | true ⓘ |
| isLargestOf | sporadic simple groups NERFINISHED ⓘ |
| isLargestSporadicSimpleGroup | true ⓘ |
| isNonAbelian | true ⓘ |
| isPerfect | true ⓘ |
| isRelatedTo |
modular functions
ⓘ
modular j-invariant ⓘ monstrous moonshine NERFINISHED ⓘ vertex operator algebras ⓘ |
| isSimple | true ⓘ |
| memberOf | sporadic groups NERFINISHED ⓘ |
| order | 808017424794512875886459904961710757005754368000000000 ⓘ |
| orderFactorization | 2^46 · 3^20 · 5^9 · 7^6 · 11^2 · 13^3 · 17 · 19 · 23 · 29 · 31 · 41 · 47 · 59 · 71 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.