Generalized category discovery (GCD) aims at grouping unlabeled samples from known and unknown classes given labeled data of known classes. To meet the recent decentralization trend in the community we introduce a practical yet challenging task Federated GCD (Fed-GCD) where the training data are distributed in local clients and cannot be shared among clients. Fed-GCD aims to train a generic GCD model by client collaboration under the privacy-protected constraint. The Fed-GCD leads to two challenges: 1) representation degradation caused by training each client model with fewer data than centralized GCD learning and 2) highly heterogeneous label spaces across different clients. To this end we propose a novel Associated Gaussian Contrastive Learning (AGCL) framework based on learnable GMMs which consists of a Client Semantics Association (CSA) and a global-local GMM Contrastive Learning (GCL). On the server CSA aggregates the heterogeneous categories of local-client GMMs to generate a global GMM containing more comprehensive category knowledge. On each client GCL builds class-level contrastive learning with both local and global GMMs. The local GCL learns robust representation with limited local data. The global GCL encourages the model to produce more discriminative representation with the comprehensive category relationships that may not exist in local data. We build a benchmark based on six visual datasets to facilitate the study of Fed-GCD. Extensive experiments show that our AGCL outperforms multiple baselines on all datasets.