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In spatial databases, the objects have semantic attributes as well as geographic coordinates. Considering the two aspects, we propose the diameter-aware extreme group query (DiaEG query), which searches for good <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-item groups of objects. We mark the <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-groups according to both semantic closenesses and geographic diameters. On the one hand, the semantic closeness ensures that in the good group the members should be close to the semantic query point <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>. On the other hand, the geographic diameter ensures that the members should be close to (or far from) each other geographically. The importances of the two aspects are evaluated by the weights <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$1-\alpha $ </tex-math></inline-formula>. Since for non-expert users it is difficult to assign an appropriate <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>, we propose two types of DiaEG queries, namely, the threshold-satisfaction query and the best-satisfaction query. The first type searches for good groups such that their total satisfaction is not smaller than a given threshold. The second type searches for the best group that has the highest satisfaction. The satisfaction of a group is the length of the <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> range, where the group keeps having the highest score. If we map the groups into the (semantic, geographic)-space, the query results are in fact the extreme points on the convex hull in the space. Using the properties of the convex hull, we propose efficient algorithms to answer two types of queries. Instead of enumerating all <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-groups, our algorithms can construct the groups incrementally and terminate once the results have been found. We conduct experiments on both real and synthetic data sets, and the experimental results show that the proposed algorithms can answer the DiaEG queries efficiently.