  We aim to reveal the physical properties and chemical composition of the
cores in the California molecular cloud (CMC), so as to better understand the
initial conditions of star formation. We made a high-resolution column density
map (18.2") with Herschel data, and extracted a complete sample of the cores in
the CMC with the \textsl{fellwalker} algorithm. We performed new
single-pointing observations of molecular lines near 90 GHz with the IRAM 30m
telescope along the main filament of the CMC. In addition, we also performed a
numerical modeling of chemical evolution for the cores under the physical
conditions. We extracted 300 cores, of which 33 are protostellar and 267 are
starless cores. About 51\% (137 of 267) of the starless cores are prestellar
cores. Three cores have the potential to evolve into high-mass stars. The
prestellar core mass function (CMF) can be well fit by a log-normal form. The
high-mass end of the prestellar CMF shows a power-law form with an index
$\alpha=-0.9\pm 0.1$ that is shallower than that of the Galactic field stellar
mass function. Combining the mass transformation efficiency ($\varepsilon$)
from the prestellar core to the star of $15\pm 1\%$ and the core formation
efficiency (CFE) of 5.5\%, we suggest an overall star formation efficiency of
about 1\% in the CMC. In the single-pointing observations with the IRAM 30m
telescope, we find that 6 cores show blue-skewed profile, while 4 cores show
red-skewed profile. [$\rm {HCO}^{+}$]/[HNC] and [$\rm {HCO}^{+}$]/$\rm
[N_{2}H^{+}]$ in protostellar cores are higher than those in prestellar cores;
this can be used as chemical clocks. The best-fit chemical age of the cores
with line observations is $\sim 5\times 10^4$~years.
