  We report on the experimental results of magnetic susceptibility, specific
heat, electron spin resonance (ESR), and high-field magnetization measurements
on a polycrystalline sample of the spin-$1/2$ distorted honeycomb-lattice
antiferromagnet Cu$_2$(pymca)$_3$(ClO$_4$). Magnetic susceptibility shows a
broad peak at about 25~K, which is typical of a low dimensional
antiferromagnet, and no long range magnetic order is observed down to 0.6~K in
the specific heat measurements. Magnetization curve up to 70~T at 1.4~K shows
triple stepwise jumps. Assuming three different exchange bonds $J_{\rm A}$,
$J_{\rm B}$ and $J_{\rm C}$ from the structure, the calculated magnetization
curve reproduces the observed one when $J_{\rm A}/k_{\rm B} = 43.7~{\rm K}$,
$J_{\rm B}/J_{\rm A} = 1$ and $J_{\rm C}/J_{\rm A} = 0.2$ except the
magnetization near 70~T, where the observed magnetization indicates another
step while the calculated magnetization becomes saturated. The relationship
between magnetization plateaus and exchange bonds is discussed based on the
numerical calculations.
