Mathieu group:M11

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Definition

This group, termed the Mathieu group of degree eleven and denoted $M_{11}$ is the subgroup of the symmetric group of degree eleven defined by the following generating set:

$M_{11}=⟨(1,2,3,4,5,6,7,8,9,10,11),(3,7,11,8)(4,10,5,6)⟩$.

Note that since both the generating permutations are even permutations, $M_{11}$ is in fact a subgroup of the alternating group of degree eleven.

This is one of the five simple Mathieu groups, which form a subset of the sporadic simple groups. The parameters for the simple Mathieu groups are $11,12,22,23,24$. There are also Mathieu groups for parameters $9,10,21$, but these are not simple groups.

GAP implementation

Definition using the MathieuGroup function

The Mathieu group has order $7920$. Unfortunately, GAP does not assign group IDs for groups of such large orders. However, this group can be defined using the MathieuGroup function, as:

MathieuGroup(11)