We study the population properties of merging binary black holes in the second LIGO-Virgo Gravitational-Wave Transient Catalog, assuming they are all forming dynamically in gravitationally bound clusters. Using a phenomenological population model, we infer the mass and spin distribution of first-generation black holes, while searching for hierarchical mergers. Considering a range of cluster masses, we see compelling evidence for hierarchical mergers for clusters with escape velocities 100 km s −1 . For our highest-likelihood cluster mass, we find that at least one catalog binary contains a second-generation black hole with > 99.99% probability, the hierarchical model is preferred over an alternative model with no hierarchical mergers (Bayes factor B = 25000), GW190521 is favored to contain two second-generation black holes with odds O > 700, and GW190517, GW190519, GW190602, GW190620, and GW190706 are mixed-generation binaries with O > 10. However, results depend strongly on the cluster escape velocity, with more modest evidence for hierarchical mergers when the escape velocity is 100 km s −1 . Assuming all binary black holes are formed dynamically in globular clusters with escape velocities on the order of tens of km s −1 , GW190519 is favored to include a second-generation black hole with odds O > 1. In this case, we find that 99% of black holes from the inferred total population are less than 48M , and that this constraint is robust under our choice of prior on the maximum black hole mass.