With recent advances in artificial intelligence (AI), research has analyzed how large language models (LLMs) can be used in brainstorming. Most studies focus on how AI can support facilitation or assist individuals. However, incorporating an AI-agent in large group brainstorming that simultaneously collaborates with multiple individuals has not been fully explored. This study explores the effects of an AI brainstorming agent (AIBA), which resembles a human brainstorming participant as closely as possible, on large group brainstorming. Therein, we developed and evaluated a prototype of such an agent in an experiment with 42 brainstorming participants. The results indicate that AIBA contributed to generating a greater variety of covered topics and increased the novelty of ideas, leading to an expansion of the solution space and a potential reduction in production deficits. By deriving design lessons, this research also provides insights into the design of AI-agents for large group brainstorming.