  Recent experiments demonstrate the production of many thousands of neutral
atoms entangled in their spin degrees of freedom. We present a criterion for
estimating the amount of entanglement based on a measurement of the global
spin. It outperforms previous criteria and applies to a wide class of entangled
states, including Dicke states. Experimentally, we produce a Dicke-like state
using spin dynamics in a Bose-Einstein condensate. Our criterion proves that it
contains at least genuine 28-particle entanglement. We infer a generalized
squeezing parameter of -11.4(5) dB.
