Minimal-order groups with an irreducible character of degree p or p²

Key Points

• Finite groups of minimal order are classified based on the presence of irreducible characters of degree p or p^2.
• The research identifies prime number conditions affecting group structure and character degrees.
• A focus on representations illuminates the significance of irreducible characters in abstract algebra.
• Understanding these groups enriches the study of complex characters and their applications within group theory.