do they have a garrison?
Yes, the U.S. Army Garrison.
United States Military Academy
As an active-duty U.S. Army installation, there are several regular Army units that provide support for the USMA and the West Point installation. 
if you graduate from west point what rank are you Second lieutenant. where is the 'united states military academy' located? West Point, New York. when was it founded? 1801. by whom? Thomas Jefferson . what do you need to gain admission? Candidates for admission must apply directly to the academy and receive a nomination, usually from a member of Congress. Other nomination sources include the president and vice president. what type of trainings does one receive here? Moral and ethical trainings. what kind of activities are performed here? Various extracurricular activities including 113 athletic and non-sport clubs are available . which sports are played? Football, ice hockey, lacrosse and basketball. name a tradition that they follow UNANSWERABLE what is the purpose of the cullum number? It is a reference and identification number assigned to each graduate. which award is distributed here? The Sylvanus Thayer Award. how can one achieve it? It honors an outstanding citizen whose service and accomplishments in the national interest exemplify the academy's motto, "Duty, Honor, Country." Currently, the award guidelines state that the recipient not be a graduate of the academy. name a few of their notable alumni Ulysses S. Grant , Dwight D. Eisenhower, Anastasio Somoza Debayle,  Fidel V. Ramos, José María Figueres  and others. who all have been commemorated? George H. W. Bush, Colin Powell, Tom Brokaw, Sandra Day O'Connor, Henry Kissinger and others have been commemorated with the Thayer Award. what competitions do they have? The Goat- Engineer game. what does it entail? It is a game between the "Goats" (the bottom half of the senior (Firstie) class academically), and the "Engineers" (the top half). The game is played with full pads and helmets using eight-man football rules.
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United States Military Academy [SEP] West Point Garrison and Stewart Army Subpost
As an active-duty U.S. Army installation, there are several regular Army units that provide support for the USMA and the West Point installation. The U.S. Army Garrison includes a Headquarters and Headquarters Company, Provost Marshal and Military Police, Religious Program Support, Keller Army Community Hospital, the West Point Dental Activity, the USMA Band (a regular Army band—USMA cadets are not members of the USMA band), and the Directorate of Human Resources (DHR). The DHR is the higher headquarters for: Military Personnel Division (MPD), Army Continuing Education System (ACES), Administrative Services Division (ASD) and the Army Substance Abuse Program (ASAP). The 1st Battalion, 1st Infantry Regiment (1–1 INF) and the 2d Army Aviation Detachment, both stationed on nearby Stewart Army Subpost, provide military training and aviation support to the USMA and the West Point Garrison.