  For $G$ a closed subgroup of $S_{\infty}$, we provide an explicit
characterization of the greatest $G$-ambit. Using this, we provide a precise
characterization of when $G$ has metrizable universal minimal flow. In
particular, each such instance fits into the framework of metrizable flows
developed by Kechris-Pestov-Todorcevic and Nguyen Van Th\'e; as a consequence,
each $G$ with metrizable universal minimal flow has the generic point property.
