Mathieu group:M11

In terms of $$M_{12}$$
This group, termed the Mathieu group of degree eleven and denoted $$M_{11}$$ is the subgroup of the symmetric group of degree eleven defined as the isotropy subgroup of any point under the natural action of Mathieu group:M12 on the projective line over field:F11.

$$M_{11}$$ is in fact a subgroup of the alternating group of degree eleven.

Relation with Mathieu groups
This is one of the five simple member of family::Mathieu groups, which form a subset of the member of family::sporadic simple groups. The parameters for the simple Mathieu groups are $$11, 12, 22, 23, 24$$. There are also Mathieu groups for parameters $$9,10$$, but these are not simple groups. The Mathieu group for parameter $$21$$ is a simple group that is not a sporadic simple group, it is isomorphic to the projective special linear group:PSL(3,4).

GAP implementation
The Mathieu group has order 7920. Unfortunately, GAP's SmallGroup library is not available for this order. The group can be constructed in either of these ways: