From inmates in prison gangs to soldiers in elite units, the intimidating reputation of groups often precedes its members. While individual reputation is known to affect people's aggressiveness, whether one's group reputation can similarly influence behavior in conflict situations is yet to be established. Using an economic game experiment, we isolate the effect of group reputation on aggression and conflict from that of individual reputation. We find that group reputation can increase the willingness to inflict costs on others but only when individuals are able to punish their fellow members. Even if internal discipline can sustain their shared reputation, more intimidating groups provide fewer benefits to their members in the short run. Using an agent-based simulation, we show that this might not be the case in the long run. Our findings yield insights into the effects of group reputation on aggression, conflict, and possible consequences for group survival.