Benefiting from the powerful capabilities of large language models (LLMs), agents based on LLMs have shown the potential to address domain-specific tasks and emulate human behaviors. However, the content generated by these agents remains somewhat superficial, owing to their limited domain expertise and the absence of an effective cognitive architecture. To address this, we present the Configurable General Multi-Agent Interaction (CGMI) framework, designed to replicate human interactions in real-world scenarios. Specifically, we propose a tree-structured methodology for the assignment, detection, and maintenance of agent personality. Additionally, we designed a cognitive architecture equipped with a skill library based on the ACT* model, which contains memory, reflection, and planning modules. We have also integrated general agents to augment the virtual environment's realism. Using the CGMI framework, we simulated numerous classroom interactions between teacher and students. The experiments indicate that aspects such as the teaching methodology, curriculum, and student performance closely mirror real classroom settings. We will open source our work.