Those allegedly involved were all in their 20s and from different parts of California, including the Bay Area and Fresno County.
In a statement, the San Francisco Giants said: "This was a horrible and intolerable display of behavior. SFPD made multiple arrests and those involved will be banned from the park."
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While arrests have been made, police say this remains an open and active investigation.
Anyone with information is asked to contact SFPD at 415-575-4444 or text a tip to TIP411.