Fischer–Griess Monster
E656672
The Fischer–Griess Monster is the largest sporadic simple group in finite group theory, a vast and highly complex algebraic structure central to the classification of finite simple groups.
Statements (65)
| Predicate | Object |
|---|---|
| instanceOf |
algebraic structure
ⓘ
finite simple group ⓘ group (mathematics) ⓘ sporadic simple group ⓘ |
| actsOn | 196883-dimensional complex vector space ⓘ |
| alsoKnownAs |
Friendly Giant
NERFINISHED
ⓘ
Monster group NERFINISHED ⓘ the Monster NERFINISHED ⓘ |
| belongsTo | sporadic groups NERFINISHED ⓘ |
| centralTo | classification of finite simple groups ⓘ |
| constructedBy | Robert Griess NERFINISHED ⓘ |
| constructionYear | 1980 ⓘ |
| hasAutomorphismGroup | itself ⓘ |
| hasElementOrder |
11
ⓘ
13 ⓘ 17 ⓘ 19 ⓘ 2 ⓘ 23 ⓘ 29 ⓘ 3 ⓘ 31 ⓘ 41 ⓘ 47 ⓘ 5 ⓘ 59 ⓘ 7 ⓘ 71 ⓘ |
| hasNontrivialSmallRepresentationDimension | 196883 ⓘ |
| hasOuterAutomorphisms | false ⓘ |
| hasPrimeDivisor |
11
ⓘ
13 ⓘ 17 ⓘ 19 ⓘ 2 ⓘ 23 ⓘ 29 ⓘ 3 ⓘ 31 ⓘ 41 ⓘ 47 ⓘ 5 ⓘ 59 ⓘ 7 ⓘ 71 ⓘ |
| hasTrivialCenter | true ⓘ |
| hasTrivialRepresentationDimension | 1 ⓘ |
| isFullAutomorphismGroupOf | Griess algebra NERFINISHED ⓘ |
| isLargest |
sporadic group by order
ⓘ
sporadic simple group ⓘ |
| isNonAbelian | true ⓘ |
| isPerfectGroup | true ⓘ |
| isSimple | true ⓘ |
| isSubgroupOf | automorphism group of the Griess algebra ⓘ |
| minimalFaithfulComplexRepresentationDimension | 196883 ⓘ |
| numberOfConjugacyClasses | 194 ⓘ |
| order | 808017424794512875886459904961710757005754368000000000 ⓘ |
| orderFactorization | 2^46 · 3^20 · 5^9 · 7^6 · 11^2 · 13^3 · 17 · 19 · 23 · 29 · 31 · 41 · 47 · 59 · 71 ⓘ |
| predictedBy |
Bernd Fischer
NERFINISHED
ⓘ
Robert Griess NERFINISHED ⓘ |
| relatedTo |
Griess algebra
NERFINISHED
ⓘ
modular function j ⓘ monstrous moonshine NERFINISHED ⓘ moonshine module ⓘ |
| symbol | M NERFINISHED ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.