We observe vacuum Rabi splitting in a lossy nearly confocal cavity indicating the strong coupling regime, despite a weak single-atom single-mode coupling. Strong collective interaction manifests itself in the typical $sqrt{N}$-dependence of the normal mode splitting on the number of atoms $N$. The $TEM_{00}$-mode coupling parameters are $(g,kappa,gamma)=2pitimes(0.12,0.8,2.6)$ MHz and up to $(1.33pm 0.08)times10^5$ cesium atoms were loaded into the mode volume.
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