In human-robot interaction, communication robots must simultaneously consider interaction with a group of people in real environments such as stations and museums. To interact with the group simultaneously, it is important to estimate whether a group's state is suitable for the robot's intended task. This paper presents a method that estimates the states of the group of people for interaction between a communication robot and the group of people by focusing on the position relationships between clusters of people. In addition, we also focused on the position relationships between clusters of people and the robot. The proposed method extracts the feature vectors from position relationships between the group of people and the robot and then estimates the group states by using Support Vector Machine with extracted feature vectors. We investigate the performance of the proposed method through a field experiment whose results achieved an 81.4% successful estimation rate for a group state. We believe these results will allow us to develop interactive humanoid robots that can interact effectively with groups of people.