AGN properties of the cluster population. Top: mean number of AGN matches per cluster (left) and mean 150 MHz radio luminosity of the brightest associated AGN (right) as a function of cluster richness. Middle panel: the relationship of richness with redshift (left) and host-galaxy K_S magnitude (right) for the same richness bins as the top panel. Bottom: mean radio luminosity versus richness as plotted in the top panel, but separated into two bins of host-galaxy magnitude (pink corresponding to −26 <  K_S <  −23.5 and orange corresponding to −23.5 <  K_S <  −21.0, where −23.5 is the median value.