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GroupTheory[FischerGroup]

Calling Sequence

FischerGroup( n )

Parameters

n

-

: {22,23,24} : integer parameter indicating the Fischer group

Description

• 

The Fischer groups are three among the sporadic finite simple groups. They were discovered by Bernd Fischer in the 1970s, and are generated by a conjugacy class of involutions, the product of any two of which has order either 2 or 3. The group Fi24' is the derived subgroup (of index 2) of a non-simple group Fi24 of order 2510411418381323442585600.

• 

The FischerGroup( n ) command returns a permutation group isomorphic to the Fischer group Fi22, Fi23 or Fi24' for n = 22, 23, 24, respectively.

Examples

withGroupTheory:

G:=FischerGroup23

G:=Fi23

(1)

DegreeG

31671

(2)

GroupOrderG

4089470473293004800

(3)

IsSimpleG

true

(4)

See Also

GroupTheory[Degree], GroupTheory[GroupOrder], GroupTheory[IsSimple]


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