Explanations can help users to better understand why items have been recommended. Additionally, explanations for group recommender systems need to consider further goals than single-user recommender systems. For example, we need to balance group members' need for privacy with their need for transparency, since a transparent explanation might pose a privacy hazard. In an online experiment with real groups (n=114 participants: 38 groups of size 3), we seek to understand which factors influence people's privacy concerns when a single explanation is presented to a group in the tourism domain. In particular, we study the direct effects of three factors on privacy concern: a) group members' personality (using the ĝ€ Big Five' personality traits), b) specific preference scenarios (i.e., having minority or majority preferences compared to two other group members), c) the type of relationship they have in the group (i.e., loosely coupled heterogeneous, versus tightly coupled homogeneous). We find that for personality two traits, Extroversion, and Agreeableness, each significantly affects the privacy concern. Moreover, having the minority or majority preferences in the group, as well as the type of relationship people have in the group, have a strong and significant influence on participants' privacy concern. These results suggest that explanations presented to groups need to be adapted to all three factors (personality, type of relationship, and preference scenario) when considering the privacy concern of users.