Group re-identification (G-ReID) aims to re-identify a group of people that is observed from non-overlapping camera systems. The existing literature has mainly addressed RGB-based problems, but RGB-infrared (RGB-IR) cross-modality matching problem has not been studied yet. In this paper, we propose a metric learning method Closest Permutation Matching (CPM) for RGB-IR G-ReID. We model each group as a set of single-person features which are extracted by MPANet, then we propose the metric Closest Permutation Distance (CPD) to measure the similarity between two sets of features. CPD is invariant with order changes of group members so that it solves the layout change problem in G-ReID. Furthermore, we introduce the problem of G-ReID without person labels. In the weak-supervised case, we design the Relation-aware Module (RAM) that exploits visual context and relations among group members to produce a modality-invariant order of features in each group, with which group member features within a set can be sorted to form a robust group representation against modality change. To support the study on RGB-IR G-ReID, we construct a new large-scale RGB-IR G-ReID dataset CM-Group. The dataset contains 15,440 RGB images and 15,506 infrared images of 427 groups and 1,013 identities. Extensive experiments on the new dataset demonstrate the effectiveness of the proposed models and the complexity of CM-Group. The code and dataset are available at: https://github.com/WhollyOat/CM-Group.