  We investigate low-temperature electronic properties of the nondimeric
organic superconductor
$\beta^{\prime\prime}$-(BEDT-TTF)$_4$[(H$_3$O)Ga(C$_2$O$_4$)$_3$]PhNO$_2$. By
examining ultrasonic properties, charge disproportionation (CD) without
magnetic field dependence is detected below $T_{\rm CD}$$\sim$8~K just above
the superconducting critical temperature $T_{\rm c}$$\sim$6~K. From quantum
oscillations in high fields, we find variation in the Fermi surface and mass
enhancement induced by the CD. Heat capacity studies elucidate that the
superconducting gap function is fully gapped in the Fermi surface, but
anisotropic with fourfold symmetry. We point out that the pairing mechanism of
the superconductivity is possibly dominated by charge fluctuations.
