Were you on the 9.25pm train service from London to Manchester, which also called at Milton Keynes on Sunday night?
Police have received a number of complaints from passengers and would like to hear from other travellers.
Detective Sergeant Michael Maher said: “I want to hear from anyone who was on the train, particularly in Coach E, around the time it reached Stoke, 10.40pm.
“By the accounts we have received, the group were chanting insults at other passengers, and some of these insults may have been racist.
“We are in the process of checking CCTV, but I would like to hear from any passengers who may have captured the behaviour of the group on mobile phones. Such footage could be crucial to our investigation.”
Anyone with information about the incident should contact British Transport Police, on 0800 405040, or by text, to 61016, quoting B5/PSUB of 5 March 2015.