Symmetric generation and contruction of the McL:2, the automorphism group of the McLaughlin group

We use the primitive action of the Mathieu group M-22 of degree 672 to define a free product of 672 copies of the cyclic group Z(2) extended by M-22 to form a semidirect product which we denote by P = 2(*672) : M-22. Such a semidirect product is called a progenitor. By investigating a subprogenitor of shape 2(*42) : A(7) we are led to a short relation by which to factor P. We verify that the resulting factor group is McL : 2, the automorphism group of the McLaughlin simple group, and identify it with the familiar permutation group of degree 275.