This paper demonstrates the role of group normative reputation in the promotion of an aggression reducing possession norm in an artificial society. A previous model of normative reputation is extended such that agents are given the cognitive capacity to categorise other agents as members of a group. In the previous model reputational information was communicated between agents concerning individuals. In the model presented here reputations are projected onto whole groups of agents (a form of "stereotyping"). By stereotyping, norm followers outperform cheaters (who do not follow the norm) under certain conditions. Stereotyping, by increasing the domain of applicability of a piece of reputational information, allows agents to make informed decisions concerning interactions with agents which no other agent has previously met. However, if conditions are not conducive, stereotyping can completely negate norm following behaviour. Group reputation can be a powerful mechanism, there...