Human group connectome analysis relies on combining individual connectome data to construct a single representative network which can be used to describe brain organisation and identify differences between subject groups. Existing methods adopt different strategies to select the network structural features to be retained or optimised at group level. In the absence of ground truth, however, it is unclear which structural features are the most suitable and how to evaluate the consequences on the group network of applying any given strategy. In this investigation, we consider the impact of defining a connectome as representative if it can recapitulate not just the structure of the individual networks in the cohort tested but also their dynamical behaviour, which we measured using a model of coupled oscillators. We applied the widely used approach of consensus thresholding to a dataset of individual structural connectomes from a healthy adult cohort to construct group networks for a range of thresholds and then identified the most dynamically representative group connectome as that having the least deviation from the individual connectomes given a dynamical measure of the system. We found that our dynamically representative network recaptured aspects of structure for which it did not specifically optimise, with no significant difference to other group connectomes constructed via methods which did optimise for those metrics. Additionally, these other group connectomes were either as dynamically representative as our chosen network or less so. While we suggest that dynamics should be at least one of the criteria for representativeness, given that the brain has evolved under the pressure of carrying out specific functions, our results suggest that the question persists as to which of these criteria are valid and testable.