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Object point cloud classification has drawn great research attention since the release of benchmarking datasets, such as the ModelNet and the ShapeNet. These benchmarks assume point clouds covering complete surfaces of object instances, for which plenty of high-performing methods have been developed. However, their settings deviate from those often met in practice, where, due to (self-)occlusion, a point cloud covering partial surface of an object is captured from an arbitrary view. We show in this paper that performance of existing point cloud classifiers drops drastically under the considered single-view, partial setting; the phenomenon is consistent with the observation that semantic category of a partial object surface is less ambiguous only when its distribution on the whole surface is clearly specified. To this end, we argue for a single-view, partial setting where supervised learning of object pose estimation should be accompanied with classification. Technically, we propose a baseline method of Pose-Accompanied Point cloud classification Network (PAPNet); built upon SE(3)-equivariant convolutions, the PAPNet learns intermediate pose transformations for equivariant features defined on vector fields, which makes the subsequent classification easier (ideally) in the category-level, canonical pose. By adapting existing ModelNet40 and ScanNet datasets to the single-view, partial setting, experiment results can verify the necessity of object pose estimation and superiority of our PAPNet to existing classifiers.