Finite groups in which almost all class sizes are prime numbers

Key Points

• The aim is to analyze the properties of finite groups that have primarily prime-sized conjugacy classes with few exceptions.
• Analyzed the structure of finite groups based on conjugacy class sizes.
• Identified and classified groups with exactly two composite class sizes.
• Studied arithmetical features in relation to group structures.
• Most class sizes in the studied finite groups are prime numbers.
• Only two class sizes were found to be composite, suggesting a unique structural condition.
• The findings indicate specific properties that such groups must possess.