Being determined by human social behaviour, pedestrian group dynamics may depend on "intrinsic properties" such as the purpose of the pedestrians, their personal relation, gender, age, and body size. In this work we investigate the dynamical properties of pedestrian dyads (distance, spatial formation and velocity) by analysing a large data set of automatically tracked pedestrian trajectories in an unconstrained "ecological" setting (a shopping mall), whose apparent physical and social group properties have been analysed by three different human coders. We observed that females walk slower and closer than males, that workers walk faster, at a larger distance and more abreast than leisure oriented people, and that inter-group relation has a strong effect on group structure, with couples walking very close and abreast, colleagues walking at a larger distance, and friends walking more abreast than family members. Pedestrian height (obtained automatically through our tracking system) influences velocity and abreast distance, both growing functions of the average group height. Results regarding pedestrian age show that elderly people walk slowly, while active age adults walk at the maximum velocity. Groups with children have a strong tendency to walk in a non-abreast formation, with a large distance (despite a low abreast distance). A cross-analysis of the interplay between these intrinsic features, taking in account also the effect of an "extrinsic property" such as crowd density, confirms these major results but reveals also a richer structure. An interesting and unexpected result, for example, is that the velocity of groups with children increases with density, at least in the low-medium density range found under normal conditions in shopping malls. Children also appear to behave differently according to the gender of the parent.