Fermions and bosons in nonsymmorphic PdSb2 with sixfold degeneracy

${\mathrm{PdSb}}₂$ is a candidate for hosting sixfold-degenerate exotic fermions (beyond Dirac and Weyl fermions). The nontrivial band crossing protected by the nonsymmorphic symmetry plays a crucial role in physical properties. We have grown high-quality single crystals of ${\mathrm{PdSb}}₂$ and characterized their physical properties under several stimuli (temperature, magnetic field, and pressure). While it is a diamagnetic Fermi-liquid metal under ambient pressure, ${\mathrm{PdSb}}₂$ exhibits a large magnetoresistance with continuous increase up to 14 T, which follows Kohler's scaling law at all temperatures. This implies one-band electrical transport, although multiple bands are predicted by first-principles calculations. By applying magnetic field along the [111] direction, de Haas--van Alphen oscillations are observed with frequency of 102 T. The effective mass is nearly zero ($0.045{m}₀$) with the Berry phase close to $\ensuremath{\pi}$, confirming that the band close to the $R$ point has a nontrivial character. Under quasihydrostatic pressure ($p$), evidence for superconductivity is observed in the resistivity below the critical temperature ${T}_c$. The dome-shaped ${T}_c$ versus $p$ is obtained with maximum ${T}_{\mathrm{c}}^max\ensuremath{\sim}2.9\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. We argue that the formation of Cooper pairs (bosons) is the consequence of the redistribution of the sixfold-degenerate fermions under pressure.