The holomorphic symplectic automorphism group of a Z3-orbifold K3 is (Z3)^2 ⋊ Z4, realized inside M12 and M24, and it combines with Kummer symmetries to generate M24.
Weil, Final report on contract AF 18 (603)-57 , in Oeuvres Scientifiques, vol
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Tracking the symmetries of $\mathbb Z_3$-orbifold K3s within the Mathieu groups
The holomorphic symplectic automorphism group of a Z3-orbifold K3 is (Z3)^2 ⋊ Z4, realized inside M12 and M24, and it combines with Kummer symmetries to generate M24.