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Abstract We present a four-step group-finding algorithm for the Gas in Galaxy Groups (G3) initiative, a spin-off of thez∼ 0 REsolved Spectroscopy Of a Local VolumE (RESOLVE) and Environmental COntext (ECO) surveys. In preparation for future comparisons to intermediate redshift (e.g., the LADUMA survey), we design the group finder to adapt to incomplete, shallow, or nonuniform data. We use mock catalogs to optimize the group finder’s performance. Compared to friends-of-friends (with false-pair splitting), the G3 algorithm offers improved completeness and halo-mass recovery with minimal loss of purity. Combining it with the volume-limited Hicensus data for RESOLVE and ECO, we examine the Hicontent of galaxy groups as a function of group halo mass. Group-integrated HimassM_{H I,grp}rises monotonically over halo massesM_halo∼ 10¹¹–10^14.5M_⊙, pivoting in slope atM_halo∼ 10^11.4M_⊙, the gas-richness threshold scale. We present the first measurement of the scatter in this relation, which has a median of ∼0.3 dex and is asymmetric toward lowerM_{H I,grp}. We discuss interesting tensions with theoretical predictions and prior measurements of theM_{H I,grp}–M_halorelation. In an appendix, we release RESOLVE DR4 and ECO DR3, including updates to survey redshifts, photometry, and group catalogs, as well as a major expansion of the ECO Hiinventory with value-added data products.