  The Hamiltonian of the simplest super $p$-brane model preserving 3/4 of the
D=4 N=1 supersymmetry in the centrally extended symplectic superspace is
derived and its symmetries are described. The constraints of the model are
covariantly separated into the first- and the second-class sets and the Dirac
brackets (D.B.) are constructed. We show the D.B. noncommutativity of the super
$p$-brane coordinates and find the D.B. realization of the $OSp(1|8)$
superalgebra. Established is the coincidence of the D.B. and Poisson bracket
realizations of the $OSp(1|8)$ superalgebra on the constraint surface and the
absence there of anomaly terms in the commutation relations for the quantized
generators of the superalgebra.
