Collective decision-making processes emerge from social feedback networks within a group. Many studies on collective behaviour underestimate the role of individual personality and, as a result, personality is rarely analysed in the context of collective dynamics. Here, we show evidence of sheltering behaviour personality in a gregarious insect (Periplaneta americana), which is characterized by a collective personality at the group level. We also highlight that the individuals within groups exhibited consistent personality traits in their probability of sheltering and total time sheltered during the three trials over one week. Moreover, the group personality, which arises from the synergy between the distribution of behaviour profiles in the group and social amplifications, affected the sheltering dynamics. However, owing to its robustness, personality did not affect the group probability of reaching a consensus. Finally, to prove social interactions, we developed a new statistical method that will be helpful for future research on personality traits and group behaviour. This approach will help to identify the circumstances under which particular group compositions may improve the fitness of individuals in gregarious species.