  We have determined possible cluster members of the nearby open cluster
Praesepe (M44) based on J and K photometry and proper motions from the PPMXL
catalogue and z photometry from the Sloan Digital Sky Survey (SDSS). In total
we identified 893 possible cluster members down to a magnitude of J = 15.5 mag,
corresponding to a mass of about 0.15 Msun for an assumed cluster distance
modulus of (m-M)_0 = 6.30 mag (d ~ 182 pc), within a radius of 3.5{\deg} around
the cluster centre. We derive a new cluster centre for Praesepe
({\alpha}_centre = 8h 39m 37s, {\delta}_centre = 19{\deg} 35' 02"). We also
derive a total cluster mass of about 630 Msun and a 2D half-number and
half-mass radius of 4.25 pc and 3.90 pc respectively. The global mass function
(MF) of the cluster members shows evidence for a turnover around m = 0.65 Msun.
While more massive stars can be fit by a power-law {\xi}(m) ~ m^(-{\alpha})
with slope {\alpha} = 2.88 +/- 0.22, stars less massive than m = 0.65 Msun are
best fitted with {\alpha} = 0.85 +/- 0.10. In agreement with its large
dynamical age, we find that Praesepe is strongly mass segregated and that the
mass function slope for high mass stars steepens from a value of {\alpha} =
2.32 +/- 0.24 inside the half-mass radius to {\alpha} = 4.90 +/- 0.51 outside
the half-mass radius. We finally identify a significant population of binaries
and triples in the colour-magnitude diagram of Praesepe. Assuming non-random
pairing of the binary components, a binary fraction of about 35% for primaries
in the mass range 0.6 < m/Msun < 2.20 is required to explain the observed
number of binaries in the colour-magnitude diagram (CMD).
