French sense of prefecture
In France, a préfecture is the capital city of a département. By extension, it is also the name of one of the governing bodies of the département. The civil servant in charge is the préfet. The préfecture is an administration that belongs to the Interior ministry, and is therefore in charge of the delivery of the identity card, driving licenses, passports, residence and work permits for foreigners, car registration, registration of the associations (creation, status modification, dissolution), and of the management of the police and of the firefighters. The préfet can make arrêtés, which are legal texts written for the application of the law, e.g. to close a building that is not conform to the safety rules, or to modify the circulation rules on the streets (speed limit, authorisation for roadworks).
The other governing body is the Conseil Général, which is in charge of the building and maintenance of schools and roads, the financial assistance to dependent people (disabled, old persons), promotion of the economical local development...
Préfecture It is also the name of the building where the préfet is based.
There are 100 préfectures in France.
There is an exception with Paris (which is itself a département) and the three surrounding départements (called the petite couronne, small crown): those four départements are governed by a single préfecture which is the préfecture de police (PP). The préfet de police has the power of law enforcement for Paris, which is a power of the mayor for the other french cities and towns. Until 1977, Paris had indeed no mayor and was entirely ruled by the préfet de police (a situation inherited from the Paris Commune, 1871).
The départements are divided into arrondissements, themselves divided into cantons. The capital city of a canton is the sous-préfecture (note that the word "arrondissement" is barely used in this meaning, this subdivision has not a big importance in France). The civil servant in charge is the sous-préfet. The capital city of a canton is a chef-lieu de canton.
Other meanings of prefecture
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See also: Subprefecture -- Politics of Japan -- Politics of China -- Politics of Taiwan -- County