• READ MORE: Scott Macnab: Sectarian laws were doomed to fail
A group of four men and one woman boarded the service at Preston station at 12.50pm and began singing sectarian and transphobic songs, which included degrading remarks about transgender people, throughout the journey.
The incident happened on Sunday 12 November on board the 9.45am service from Euston to Glasgow Central station.
Officers are appealing to speak to anyone who was travelling on the service and witnessed what happened and what was said by the group.
Any information big or small could help officers investigating the incident. Please call 0800 40 50 40 or text 61016 citing reference 253 - 12/11/17.