Fraud detection, a classical data mining problem in finance applications, has risen in significance amid the intensifying confrontation between fraudsters and anti-fraud forces. Recently, an increasing number of criminals are constantly expanding the scope of fraud activities, threatening the property of innocent victims from various groups. However, most existing approaches treat the node entities in these diverse transaction groups equally, which leads to underutilization of information within the various group patterns. This poses significant challenges to protecting multiple transaction groups simultaneously. Therefore, in this paper, we propose a novel group-enhanced multi-relation graph neural network-based model, named GEM-GNN, to address the important defects of existing fraud detection models in the diverse transaction groups situation. In particular, we utilize multi-relation graphs and rule-based group classifier from historical transactions and then apply a group enhancement module based on parallel multiple neutral networks to capture diverse patterns from transaction groups. Extensive experiments the public datasets demonstrate that our method not only significantly outperforms baselines, but also effectively leverages the information within group patterns.