You are the "new sheriff in town". Exert your authority. End the era of "feeling good" and focus on the responsibilities of providing service to your stakeholders.
I would recommend that you hold a meeting with your subordinates and point out what you have observed: laziness, lack of teamwork, and tons of personality conflicts. Outline your expectations. Indicate that you are there to assist in resolving problems (in problem-solving sessions, one-on-one, or in groups encourage the employees to come up with solutions - they will more readily 'buy into' implementation), and listen to suggestions on how to make the workplace more efficient and effective.
Explain that noncompliance will result in discipline (for the purpose of rehabilitation and correcting unacceptable behavior, not retribution), in four steps for minor infractions: Verbal counseling, written warning, suspension (usually 3 days starting on Tuesday - no reason to provide an extended weekend), and submission of an undated letter of resignation (date to be filled in by you at a later time if necessary).
In serious cases, such as insubordination, fighting, destruction of property, being under the influence of alcohol/drugs, etc., immediate discharge is warranted.
Keep the Human Resources Department apprised of your intended actions before you take them; HR may have some alternative recommendations.
Hope this helps.