set the flux limit $i < 24.0$. We find 34 clusters and 7952 cluster galaxies from the mock catalog. For the first test, we stack photo-$z$ galaxies around these 34 clusters, subtract the background, and then compute the composite surface density as a function of $r_p$. We then compare the composite surface density from real group galaxies and from the recovered sample. The result is shown in Figure \[f1\]. In this case, the background sample is selected from random positions. The recovered surface density agrees well with the real surface density within 1 but at large radii beyond 1 , it exhibits a small excess with large error bars.

The other test shown in Figure \[f2\] displays the rest-frame $g$ minus $r$ color, $(g-r)_0$, as a function of the projected group-centric radius $r_p$ as a two-dimensional color-coded number count map for the real group galaxies (upper-left panel), stacked galaxies (upper-right panel), normalized field galaxies (bottom-left panel), and residual (bottom-right panel), defined as the difference between real and recovered galaxy sample. The stacked galaxy sample is distinct from the real galaxy sample. However, after we subtract the normalized background sample from the stacked galaxy sample, the recovered sample shows similar structure 