This study investigates the Horizontal-Vertical Individualism-Collectivism (HVIC) traits of Large Language Models (LLMs), addressing the gap in understanding their cultural and social cognition. HVIC, a cross-cultural psychology framework, offers insights into cognitive patterns shaped by culture. We systematically evaluate multiple LLMs using quantitative (INDCOL scale) method, assessing their intrinsic HVIC traits and ability to simulate cultural and gender-based differences. Our findings reveal LLMs' capacity to capture HVIC nuances, providing a unique lens for studying human cognition through human-LLM comparisons. This research contributes to developing culturally sensitive AI systems and offers new perspectives on human HVIC traits, advancing both theoretical understanding and practical applications of AI.