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GroupTheory

  

ConwayGroup

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

ConwayGroup( n )

Parameters

n

-

: {1,2,3} : integer parameter selecting the Conway group

Description

• 

The Conway groups Co1, Co2 and Co3 are sporadic finite simple groups, discovered by John H. Conway in the 1960s.

• 

The largest Conway group Co1 is the quotient of the automorphism group of the Leech lattice (a certain 24-dimensional unimodular lattice) by its center (of order 2), and has order equal to 4157776806543360000.

• 

The second Conway group Co2 has order equal to 42305421312000, and is the group of automorphisms of the Leech lattice fixing a vector of length 2.

• 

The third Conway group Co3 has order equal to 495766656000, and can be described as the group of automorphisms of the Leech lattice fixing a vector of length 6.

• 

The ConwayGroup( n ) command returns a permutation group isomorphic to the Conway group Con, for n = 1,2,3.

Examples

withGroupTheory:

GConwayGroup2

G:=Co2

(1)

DegreeG

2300

(2)

GroupOrderG

42305421312000

(3)

IsSimpleG

true

(4)

Compatibility

• 

The GroupTheory[ConwayGroup] command was introduced in Maple 17.

• 

For more information on Maple 17 changes, see Updates in Maple 17.

See Also

GroupTheory[Degree]

GroupTheory[GroupOrder]

GroupTheory[IsSimple]

 


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