Mathieu group:M22

Definition
This is the member of family::Mathieu group of degree 22, denoted $$M_{22}$$, and is the subgroup of the symmetric group of degree 22 generated by the following permutations:

$$M_{22} := \langle (1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22), (1,4,5,9,3)(2,8,10,7,6)(12,15,16,20,14)(13,19,21,18,17), (1,21)(2,10,8,6)(3,13,4,17)(5,19,9,18)(11,22)(12,14,16,20) \rangle$$

GAP implementation
GAP's SmallGroup library is not available for this large order.