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- Sporadic groups

Sporadic group

In mathematics, a sporadic group is one of the 26 exceptional groups found in the classification of finite simple groups. A simple group is a group G that does not have any normal subgroups except for

Suzuki sporadic group

In the area of modern algebra known as group theory, the Suzuki group Suz or Sz is a sporadic simple group of order 213 · 37 · 52 · 7 · 11 · 13 = 448345497600≈ 4×1011.

Monster group

In the area of abstract algebra known as group theory, the monster group M (also known as the Fischer–Griess monster, or the friendly giant) is the largest sporadic simple group, having order 246 ·

Monstrous moonshine

In mathematics, monstrous moonshine, or moonshine theory, is the unexpected connection between the monster group M and modular functions, in particular, the j function. The term was coined by John Con

McLaughlin sporadic group

In the area of modern algebra known as group theory, the McLaughlin group McL is a sporadic simple group of order 27 ⋅ 36 ⋅ 53 ⋅ 7 ⋅ 11 = 898,128,000≈ 9×108.

Janko group J3

In the area of modern algebra known as group theory, the Janko group J3 or the Higman-Janko-McKay group HJM is a sporadic simple group of order 27 · 35 · 5 · 17 · 19 = 50232960.

O'Nan group

In the area of abstract algebra known as group theory, the O'Nan group O'N or O'Nan–Sims group is a sporadic simple group of order 29 · 34 · 5 · 73 · 11 · 19 · 31= 460815505920≈ 5×1011.

Mathieu group M12

In the area of modern algebra known as group theory, the Mathieu group M12 is a sporadic simple group of order 12 · 11 · 10 · 9 · 8 = 26 · 33 · 5 · 11 = 95040.

Conway group Co1

In the area of modern algebra known as group theory, the Conway group Co1 is a sporadic simple group of order 221 · 39 · 54 · 72 · 11 · 13 · 23= 4157776806543360000≈ 4×1018.

Conway group

In the area of modern algebra known as group theory, the Conway groups are the three sporadic simple groups Co1, Co2 and Co3 along with the related finite group Co0 introduced by (Conway , ). The larg

Mathieu group M23

In the area of modern algebra known as group theory, the Mathieu group M23 is a sporadic simple group of order 27 · 32 · 5 · 7 · 11 · 23 = 10200960≈ 1 × 107.

Baby monster group

In the area of modern algebra known as group theory, the baby monster group B (or, more simply, the baby monster) is a sporadic simple group of order 241 · 313 · 56 · 72 · 11 · 13 · 17 · 19 · 23 · 31

Janko group J4

In the area of modern algebra known as group theory, the Janko group J4 is a sporadic simple group of order 221 · 33 · 5 · 7 · 113 · 23 · 29 · 31 · 37 · 43= 86775571046077562880≈ 9×1019.

Miracle Octad Generator

In mathematics, the Miracle Octad Generator, or MOG, is a mathematical tool introduced by Rob T. Curtis for manipulating the Mathieu groups, binary Golay code and Leech lattice.

Janko group J2

In the area of modern algebra known as group theory, the Janko group J2 or the Hall-Janko group HJ is a sporadic simple group of order 27 · 33 · 52 · 7 = 604800≈ 6×105.

Tits group

In group theory, the Tits group 2F4(2)′, named for Jacques Tits (French: [tits]), is a finite simple group of order 211 · 33 · 52 · 13 = 17,971,200. It is sometimes considered a 27th sporadic group.

Fischer group Fi22

In the area of modern algebra known as group theory, the Fischer group Fi22 is a sporadic simple group of order 217 · 39 · 52 · 7 · 11 · 13= 64561751654400≈ 6×1013.

Mathieu groupoid

In mathematics, the Mathieu groupoid M13 is a groupoid acting on 13 points such that the stabilizer of each point is the Mathieu group M12. It was introduced by Conway and studied in detail by .

Harada–Norton group

In the area of modern algebra known as group theory, the Harada–Norton group HN is a sporadic simple group of order 214 · 36 · 56 · 7 · 11 · 19= 273030912000000≈ 3×1014.

Mathieu group

In group theory, a topic in abstract algebra, the Mathieu groups are the five sporadic simple groups M11, M12, M22, M23 and M24 introduced by Mathieu . They are multiply transitive permutation groups

Lyons group

In the area of modern algebra known as group theory, the Lyons group Ly or Lyons-Sims group LyS is a sporadic simple group of order 28 · 37 · 56 · 7 · 11 · 31 · 37 · 67= 51765179004000000≈ 5×1016.

Supersingular prime (moonshine theory)

In the mathematical branch of moonshine theory, a supersingular prime is a prime number that divides the order of the Monster group M, which is the largest sporadic simple group. There are precisely f

Leech lattice

In mathematics, the Leech lattice is an even unimodular lattice Λ24 in 24-dimensional Euclidean space, which is one of the best models for the kissing number problem. It was discovered by John Leech.

Rudvalis group

In the area of modern algebra known as group theory, the Rudvalis group Ru is a sporadic simple group of order 214 · 33 · 53 · 7 · 13 · 29= 145926144000≈ 1×1011.

Janko group J1

In the area of modern algebra known as group theory, the Janko group J1 is a sporadic simple group of order 23 · 3 · 5 · 7 · 11 · 19 = 175560≈ 2×105.

Fischer group Fi24

In the area of modern algebra known as group theory, the Fischer group Fi24 or F24′ is a sporadic simple group of order 221 · 316 · 52 · 73 · 11 · 13 · 17 · 23 · 29= 1255205709190661721292800≈ 1×1024.

Conway group Co2

In the area of modern algebra known as group theory, the Conway group Co2 is a sporadic simple group of order 218 · 36 · 53 · 7 · 11 · 23= 42305421312000≈ 4×1013.

Higman–Sims group

In the area of modern algebra known as group theory, the Higman–Sims group HS is a sporadic simple group of order 29⋅32⋅53⋅7⋅11 = 44352000≈ 4×107. The Schur multiplier has order 2, the outer automorph

Classification of finite simple groups

In mathematics, the classification of the finite simple groups is a result of group theory stating that every finite simple group is either cyclic, or alternating, or it belongs to a broad infinite cl

Mathieu group M11

In the area of modern algebra known as group theory, the Mathieu group M11 is a sporadic simple group of order 24 · 32 · 5 · 11 = 11 · 10 · 9 · 8 = 7920.

Janko group

No description available.

Fischer group

In the area of modern algebra known as group theory, the Fischer groups are the three sporadic simple groups Fi22, Fi23 and Fi24 introduced by Bernd Fischer .

Pariah group

In group theory, the term pariah was introduced by Robert Griess in to refer to the six sporadic simple groups which are not subquotients of the monster group. The twenty groups which are subquotients

II25,1

In mathematics, II25,1 is the even 26-dimensional Lorentzian unimodular lattice. It has several unusual properties, arising from Conway's discovery that it has a norm zero Weyl vector. In particular i

Conway group Co3

In the area of modern algebra known as group theory, the Conway group is a sporadic simple group of order 210 · 37 · 53 · 7 · 11 · 23= 495766656000≈ 5×1011.

Mathieu group M24

In the area of modern algebra known as group theory, the Mathieu group M24 is a sporadic simple group of order 210 · 33 · 5 · 7 · 11 · 23 = 244823040≈ 2×108.

List of finite simple groups

In mathematics, the classification of finite simple groups states that every finite simple group is cyclic, or alternating, or in one of 16 families of groups of Lie type, or one of 26 sporadic groups

Thompson sporadic group

In the area of modern algebra known as group theory, the Thompson group Th is a sporadic simple group of order 215 · 310 · 53 · 72 · 13 · 19 · 31= 90745943887872000≈ 9×1016.

Held group

In the area of modern algebra known as group theory, the Held group He is a sporadic simple group of order 210 · 33 · 52 · 73 · 17 = 4030387200≈ 4×109.

Mathieu group M22

In the area of modern algebra known as group theory, the Mathieu group M22 is a sporadic simple group of order 27 · 32 · 5 · 7 · 11 = 443520≈ 4×105.

Griess algebra

In mathematics, the Griess algebra is a commutative non-associative algebra on a real vector space of dimension 196884 that has the Monster group M as its automorphism group. It is named after mathema

Umbral moonshine

In mathematics, umbral moonshine is a mysterious connection between Niemeier lattices and Ramanujan's mock theta functions. It is a generalization of the Mathieu moonshine phenomenon connecting repres

Fischer group Fi23

In the area of modern algebra known as group theory, the Fischer group Fi23 is a sporadic simple group of order 218 · 313 · 52 · 7 · 11 · 13 · 17 · 23= 4089470473293004800≈ 4×1018.

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