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Two men were arrested following alleged racist and homophobic abuse during Gillingham's tie against Exeter last night.
Gillingham Football Club said the pair were ejected from Priestfield Stadium after the allegations were brought to the attention of stewards during the Carabao Cup match.
The club says the men will face lifetime bans from the stadium if found guilty of the offences.
Co-chairman and CEO Paul Fisher said: "There is no place for such behaviour at Gillingham Football Club, nor anywhere in society.
"We have a zero tolerance approach at a family football club such as Gillingham."
Kent Police confirmed they were notified of alleged homophobic and racist comments made during the match, and two men were arrested on suspicion of aggravated public order offences.
A 23-year-old man from London and a 19-year-old man from Dartford remain in custody pending further enquiries.
Superintendent Simon Alland said: "Kent Police has a strong working relationship with football clubs throughout the county and we support them in their efforts to eradicate abuse of all kinds from the sport.
"Any allegations of abusive behaviour motivated by hate will be fully investigated, and anyone found guilty of such offences risks receiving a custodial sentence and a banning order preventing them from watching designated football games anywhere in the country."