Mathieu group:M23

Definition
This is the member of family::Mathieu group of degree 23, denoted $$M_{23}$$, and is the subgroup of the symmetric group of degree 24 generated by the following permutations:

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

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