The task of recommending items to a group of users, a.k.a. group recommendation, is receiving increasing attention. However, the cold-start problem inherent in recommender systems is amplified in group recommendation because interaction data between groups and items are extremely scarce in practice. Most existing work exploits associations between groups and items to mitigate the data scarcity problem. However, existing approaches inevitably fail in extreme cold-start scenarios where associations between groups and items are lacking. For this reason, we design a group recommendation model for EXreme cold-star} in group REcommendation (EXTRE) suitable for the extreme cold start scenario. The basic idea behind EXTRE is to use the limit theory of graph convolutional neural networks to establish implicit associations between groups and items, and the derivation of these associations does not require explicit interaction data, making it suitable for cold start scenarios. The training process of EXTRE depends on the newly defined and interpretable concepts of consistency and discrepancy, other than commonly used negative sampling with pairwise ranking, which can improve the performance of the group recommendation. Extensive experiments validate the efficacy of the proposed model EXTRE.