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This paper generates an augmented hyperchaotic system from the famous Lorenz system. The hyperchaotic system has complex dynamic properties, including stability, periodicity, multiple coexisting attractors, period-doubling and Hopf bifurcations, and hyperchaos for different parameter conditions and all these dynamic properties are presented by detailed theoretical and numerical analysis. Moreover, the finite-time synchronization of the hyperchaotic system is considered by using the state-error controller. Both the sufficient conditions for finite-time synchronization and the corresponding finite time are strictly established.