  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.
