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Five men were involved in a disturbance at Tesco in Riverhead near Sevenoaks.
The incident happened at the store in Aisher Way at around 9pm last Thursday.
Three men got out of a small car in the car park and approached two other men who were just leaving the shop.
There was an altercation between the two groups that moved inside the store and some stock and security equipment was damaged.
Sgt Ricky O’Neill said: "We have been making inquiries to identify those involved and are now releasing images of five people who may be able to assist us with our investigation.
"Anyone who recognises any of the men is urged to call our appeal line: 01622 604100, quoting reference 46/254777/21."
The public can also call Crimestoppers anonymously on 0800 555111.