Double perovskites (DPs) offer broad compositional tunability, but predicting the space groups (SGs) of stable structures remains difficult because available datasets are often strongly imbalanced toward dominant SG classes. We introduce Dynamic and Diversity-enhanced Few-shot Retrieval and Rule-Guided Inference for Space-Group Prediction (DyRIS), an LLM-agent-based framework that predicts ranked SG candidates from a given DP composition. DyRIS uses diversity-enhanced dynamic few-shot prompting to retrieve relevant in-context examples while limiting the dominance of frequently represented SGs. It further incorporates rule-guided inference based on B/B' cation ordering, quantitative indicators, and major-SG bias control to refine and rank the final Top-3 SG candidates. We evaluate DyRIS on 3,528 thermodynamically filtered DP entries and compare it with composition-based and descriptor-based baselines. At a training-data ratio of 0.5, DyRIS achieves competitive overall accuracy while obtaining the best Overall Top-1 macro-F1 score and the best performance across all Minor-SG metrics. DyRIS improves Minor-SG Top-1 accuracy by 3.26 percentage points relative to CrabNet and achieves higher Minor-SG Top-3 accuracy than the strongest PyCaret-based baseline. Ablation studies show that diversity-enhanced retrieval, quantitative indicators, major-SG bias control, and B/B' ordering information each contribute to prediction performance. Additional experiments show that the final rule-guided inference step is not easily replaced by conventional classifier- or ranker-based models. These findings demonstrate the potential of combining retrieval-based LLM reasoning with crystallographic domain knowledge for SG prediction in imbalanced materials datasets. Blogger's Review: This paper proposes a new LLM framework DyRIS for predicting the space groups of double perovskites, achieving high accuracy through dynamic few-shot learning and rule-guided inference, especially in predicting minor SG classes, which provides new insights and methods for materials science research.