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An action of a group $G$ on an Enriques surface $S$ is called Mathieu if itacts on $H^0(2K_S)$ trivially and every element of order 2, 4 has Lefschetznumber 4. A finite group $G$ has a Mathieu action on some Enriques surface ifand only if it is isomorphic to a subgroup of the symmetric group$\mathfrak{S}_6$ of degree 6 and the order $|G|$ is not divisible by $2^4$.Explicit Mathieu actions of the three groups $\mathfrak S_5, N_{72}$ and$\mathfrak A_6$, together with non-Mathieu one of $H_{192}$, on polarizedEnriques surfaces of degree 30, 18, 10 and 6, respectively, are constructedwithout Torelli type theorem to prove the if part.

Finite groups of automorphisms of Enriques surfaces and the Mathieu group $M_{12}$