Learning a compact feature embedding is crucial for effective image representation. Current feature embedding methods, including both supervised and unsupervised approaches, rely on deep metric learning techniques that aim to pull positive samples of the same class closer and push negative samples from different classes farther apart. However, supervised metric learning methods may exhibit bias towards the ground truth labels, leading to overfitting on the training set. On the other hand, unsupervised metric learning methods could suffer from degraded performance due to the long-tailed distribution of the clusters. To address these challenges, we propose a group collaborative unsupervised deep metric learning method for feature embedding. Specifically, we train the deep feature embedding model based on the teacher-student framework. The student network produces the final compact embedding, while the teacher network generates pseudo-labels for group collaborative learning and knowledge distillation. Both networks share a similar network structure, and the parameters of the teacher network are updated using the momentum-based moving average of the parameters of the student network. Experimental results on benchmark image retrieval datasets demonstrate the effectiveness and efficiency of the proposed method, achieving an improvement in Recall@1 of up to 1.8%.