The capacity of general mobile ad hoc networks (MANETs) remains largely unknown up to now, which significantly hinders the development and commercialization of such networks. Available throughput capacity studies of MANETs mainly focus on either the order sense capacity scaling laws, the exact throughput capacity under a specific algorithm, or the exact throughput capacity without a careful consideration of critical wireless interference and transmission range issues. In this paper, we explore the exact throughput capacity for a class of MANETs, where we adopt group-based scheduling to schedule simultaneous link transmissions for interference avoidance and allow the transmission range of each node to be adjusted. We first determine a general throughput capacity upper bound for the concerned MANETs, which holds for any feasible packet delivery algorithm in such networks. We then prove that the upper bound we determined is just the exact throughput capacity for this class of MANETs by showing that for any traffic input rate within the throughput capacity upper bound, there exists a corresponding two-hop relay algorithm to stabilize such networks. A closed-form upper bound for packet delay is further derived under any traffic input rate within the throughput capacity. Finally, based on the network capacity result, we examine the impacts of transmission range and node density upon network capacity.