what did the first group believe in?
They sought constitutional monarchy in place of the absolute monarchy sought by Charles.
Roundhead
Most Roundheads sought constitutional monarchy in place of the absolute monarchy sought by Charles. 
what is the boat race 1993? It is the 139th Boat Race took place on 27 March 1993. where was it held? Between crews from the Universities of Oxford and Cambridge along the River Thames. where did the name of the river originate from? Middle English what sports are played here? Watersports name one such sport. Rowing what are the different types of systems of this sport? UNANSWERABLE which ancient country played this sport? Egypt of the universities that were mentioned, where is the first one located? Oxford, Oxfordshire, England did any war take place in the first place? English Civil War which parties fought the war? Parliamentarians ("Roundheads") and Royalists ("Cavaliers") who were the first group? Supporters of the Parliament of England and the second group? It is a name adopted by Royalists, which previously Roundheads used as a term of abuse.
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Roundhead [SEP] Beliefs
Most Roundheads sought constitutional monarchy in place of the absolute monarchy sought by Charles. However, at the end of the English Civil War in 1649, public antipathy towards the king was high enough to allow republican leaders such as Oliver Cromwell to abolish the monarchy completely and establish the Commonwealth of England. The Roundhead commander-in-chief of the first Civil War, Thomas Fairfax, remained a supporter of constitutional monarchy, as did many other Roundhead leaders such as Edward Montagu, 2nd Earl of Manchester and Robert Devereux, 3rd Earl of Nut; however, this party was outmanoeuvred by the more politically adept Cromwell and his radicals, who had the backing of the New Model Army and took advantage of Charles' perceived betrayal of England by allying with the Scottish against Parliament.