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GroupTheory

  

HeldGroup

 

Calling Sequence

Description

Examples

Compatibility

Calling Sequence

HeldGroup()

Description

• 

The Held group of order 4030387200 is one of the sporadic finite simple groups. It was discovered by Dieter Held in 1969 as a group containing an involution whose centralizer is isomorphic to the centralizer of an involution in the Mathieu group M24.  (The only other such group is the group PSL5,2 .) The construction of the Held group was later completed by Graham Higman and John McKay. The Held group can also be realized as the centralizer of an element of order 7 in the Monster.

• 

The HeldGroup() command returns either a permutation group, or a finitely presented group, isomorphic to the Held group.

Examples

withGroupTheory:

GHeldGroup

G:=He

(1)

DegreeG

2058

(2)

GroupOrderG

4030387200

(3)

IsSimpleG

true

(4)

Compatibility

• 

The GroupTheory[HeldGroup] 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]

GroupTheory[MathieuGroup]

GroupTheory[Monster]

 


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