We present the Palomar Transient Factory discoveries and the photometric and spectroscopic observations of PTF11kmb and PTF12bho. We show that both transients have properties consistent with the class of calcium-rich gap transients, specifically lower peak luminosities and rapid evolution compared to ordinary supernovae, and a nebular spectrum dominated by [Ca II] emission. A striking feature of both transients is their host environments: PTF12bho is an intra-cluster transient in the Coma Cluster, while PTF11kmb is located in a loose galaxy group, at a physical offset ~150 kpc from the most likely host galaxy. Deep Subaru imaging of PTF12bho rules out an underlying host system to a limit of $M_R > -8.0$ mag, while Hubble Space Telescope imaging of PTF11kmb reveals a marginal counterpart that, if real, could be either a background galaxy or a globular cluster. We show that the offset distribution of Ca-rich gap transients is significantly more extreme than that seen for Type Ia supernovae or even short-hard gamma-ray bursts (sGRBs). Thus, if the offsets are caused by a kick, they require larger kick velocities and/or longer merger times than sGRBs. We also show that almost all Ca-rich gap transients found to date are in group and cluster environments with elliptical host galaxies, indicating a very old progenitor population; the remote locations could partially be explained by these environments having the largest fraction of stars in the intra-group/intra-cluster light following galaxy-galaxy interactions.
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