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All spaces (and groups) are assumed to be separable and metrizable. Jan vanMill showed that every analytic group $G$ is Effros (that is, every continuoustransitive action of $G$ on a non-meager space is micro-transitive). Wecomplete the picture by obtaining the following results: under $\mathsf{AC}$,there exists a non-Effros group; under $\mathsf{AD}$, every group is Effros;under $\mathsf{V=L}$, there exists a coanalytic non-Effros group. The abovecounterexamples will be graphs of discontinuous homomorphisms.

On the scope of the Effros theorem