Mathieu group:M24

Definition
This is the member of family::Mathieu group of degree 24, denoted $$M_{24}$$, and is the subgroup of the symmetric group of degree 24 generated by the following permutations:

$$M_{24} := \langle (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23), (3,17,10,7,9)(4,13,14,19,5)(8,18,11,12,23)(15,20,22,21,16), (1,24)(2,23)(3,12)(4,16)(5,18)(6,10)(7,20)(8,14)(9,21)(11,17)(13,22)(15,19) \rangle$$

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