Large Language Models (LLMs) have been observed to encode and perpetuate harmful associations present in the training data. We propose a theoretically grounded framework called StereoMap to gain insights into their perceptions of how demographic groups have been viewed by society. The framework is grounded in the Stereotype Content Model (SCM); a well-established theory from psychology. According to SCM, stereotypes are not all alike. Instead, the dimensions of Warmth and Competence serve as the factors that delineate the nature of stereotypes. Based on the SCM theory, StereoMap maps LLMs' perceptions of social groups (defined by socio-demographic features) using the dimensions of Warmth and Competence. Furthermore, the framework enables the investigation of keywords and verbalizations of reasoning of LLMs' judgments to uncover underlying factors influencing their perceptions. Our results show that LLMs exhibit a diverse range of perceptions towards these groups, characterized by mixed evaluations along the dimensions of Warmth and Competence. Furthermore, analyzing the reasonings of LLMs, our findings indicate that LLMs demonstrate an awareness of social disparities, often stating statistical data and research findings to support their reasoning. This study contributes to the understanding of how LLMs perceive and represent social groups, shedding light on their potential biases and the perpetuation of harmful associations.