Applications of Large Language Models (LLMs) increasingly involve collaborative tasks where multiple agents interact, forming “LLM societies.” In this context, we explore whether large groups of LLMs exhibit emergent group behaviors similar to those in human societies. First, by simulating social network formation, we observe that LLMs spontaneously form scale-free networks. Agents connect through linear preferential attachment, mirroring the Barabasi-Albert model and real-world social networks. Second, we investigate the ability of LLMs to reach a consensus on arbitrary norms without external preferences, thereby self-regulating their behavior. In human societies, consensus without institutions is limited by cognitive capacities. Similarly, we find that LLMs can reach consensus, with the opinion dynamics described by a majority force coefficient determining the consensus likelihood. This majority force strengthens with higher language understanding but decreases with larger group sizes, resulting in a critical group size beyond which consensus becomes unattainable. For more advanced LLMs, this critical size grows exponentially with language capabilities, exceeding the typical length