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Omaha beach was seized by the US 1st Infantry Division along with the 116th Infantry Brigade Team (29th Infantry Division) and the 16th Infantry Brigade Team (1st Infantry Division). US Army Rangers also took part in the invasion force.
LCI's (landing craft infantry)
Approximately 39,000 soldiers of the US 1st and 29 th Infantry Divisions were at Omaha Beach.
Omaha Beach was the landing zone for the US 1st Infantry & US 29th Infantry Divisions on D-Day. British units were not assigned the mission of landing and seizing the beach there. It is always possible that British soldiers, sailors, airmen could have been assigned tasks working with the Americans (liason, fire control, beach masters, UDT, etc.) during the inital stages of the invasion. Also during the time that troops were brought on-shore after the landing area was secure, days later, it is possible that some British, Canadian, French, or other units first arrived at Omaha Beach.
Well it was the 1st Infantry and 29th Infantry Divisions. I am out sure of the individual regiments at the time.
Omaha and Utah were the American beaches.
The US 1st Infantry Division and the US 29th Infantry Division (Virginia-Maryland National Guard).
Approximately 40,000 soldiers of the 1st and 29th US Infantry Divisions and other attached units were to land on Omaha Beach with 3,500 vehicles.
Troops of the U.S. Army's 1st and 29th Infantry Divisions and the 2nd Ranger Battalion.
On Omaha Beach, one of the two American landing zones. "Omaha" is the Allied code name for that location. The US 1st Infantry Division & the US 29th Infantry Division (Maryland-Virginia National Guard) assaulted that beach on D-Day.
Some of this information is available from the British Ministry of Defence or the US Defense Department. (see related link)
There were 5 Beaches. Gold, Juno & Sword were British/Canadian/British. Utah & Omaha were US. Omaha was referred to as 'Bloody Omaha' because of the (Relatively) high casualty rate, the infantry were caught in enfilade fire from the defenders, but it was still a successful landing.