to construct the larger ones. John Conway has shown that one can also extend this sequence up, obtaining the Mathieu groupoid ''M''₁₃ acting on 13 points. M₂₁ is simple, but is not a sporadic simple group, being isomorphic to the projective special linear group PSL(3,4).

History

introduced the group M₁₂ as part of an investigation of multiply transitive permutation