Considering that the interaction topology among agents contains both cooperative and competitive relationships, the group consensus control problem for second-order multi-agent systems is investigated. A distributed finite-time leader-following group consensus algorithm based on event-triggered control mechanisms is proposed. The proposed control protocol can drive the second-order system to achieve group consensus within a finite settling time. Specifically speaking, agents in the same subgroup converge to an identical consensus value and converge to different ones if they belong to different subgroups. An event-triggered control mechanism is adopted to reduce the update frequency of the controller and further conserve energy consumption. The finite-time stability condition is derived based on the algebraic graph theory and the Lyapunov stability theory. An explicit estimation of the finite convergence time is deduced by subtly constructing the Lyapunov function. Rigorous proof shows that the lower bound of the two consecutive triggering time intervals is strictly positive, thus excluding the undesirable Zeno behavior. The simulation example illustrates the effectiveness of the theoretical results.