A small group is a fundamental interaction unit for achieving a shared goal. Group performance can be automatically predicted using computational methods to analyze members' verbal behavior in task-oriented interactions, as has been proven in several recent works. Most of the prior works focus on lower-level verbal behaviors, such as acoustics and turn-taking patterns, using either hand-crafted features or even advanced endto-end methods. However, higher-level group-based communicative functions used between group members during conversations have not yet been considered. In this work, we propose a two-stage training framework that effectively integrates the communication function, as defined using Bales' interaction process analysis (IPA) coding system, with the embedding learned from the low-level features in order to improve the group performance prediction. Our result shows a significant improvement compared to the state-of-the-art methods (4.241 MSE and 0.341 Pearson's correlation on NTUBA-task1 and 3.794 MSE and 0.291 Pearson's correlation on NTUBA-task2) on the NTUBA (National Taiwan University Business Administration) small-group interaction database. Furthermore, based on the design of IPA, our computational framework can provide a time-grained analysis of the group communication process and interpret the beneficial communicative behaviors for achieving better group performance.