Final answer:
Flexibility is not a characteristic of bureaucracy; instead, bureaucracies are known for their hierarchy, division of labor, explicit rules, and impersonality.
Step-by-step explanation:
The characteristic that is not a feature of a bureaucracy is Flexibility. Bureaucracies, as characterized by the sociologist Max Weber, typically have a hierarchy of authority, a clear division of labor, explicit rules, and a sense of impersonality. They are designed to be efficient and standardized organizations, which means that they are often rigid and not particularly adaptable to unique or new situations.