  Ferromagnetic quantum critical points were predicted to be prohibited in
clean itinerant ferromagnetic systems, yet such a phenomenon was recently
revealed in CeRh$_6$Ge$_4$, where the Curie temperature can be continuously
suppressed to zero under a moderate hydrostatic pressure. Here we report the
observation of quantum oscillations in CeRh$_6$Ge$_4$ from measurements using
the cantilever and tunnel-diode oscillator methods in fields up to 45 T,
clearly demonstrating that the ferromagnetic quantum criticality occurs in a
clean system. In order to map the Fermi surface of CeRh$_6$Ge$_4$, we performed
angle-dependent measurements of quantum oscillations at ambient pressure, and
compared the results to density functional theory calculations. The results are
consistent with the Ce 4f electrons remaining localized, and not contributing
to the Fermi surface, suggesting that localized ferromagnetism is a key factor
for the occurrence of a ferromagnetic quantum critical point in CeRh$_6$Ge$_4$.
