The incident happened shortly after 2.10pm on Tuesday, 10 March, as a 23-year-old woman travelled with her friend on a Leeds to Liverpool Lime Street service, according to police.
Appealing for information about from other passengers on the train, Pc Colin Steele of British Transport Police said: “As the train made its way between Leeds and Dewsbury the victim and her friend were both touched by a man who moved close to both of them.
“They were able to move away, but the incident left both women shaken.”
“The behaviour of the men was absolutely outrageous and I am calling on anyone with information about the incident to come forward.”
He added: “I’ve also managed to isolate an image of a man who, I believe, has vital information about what happened – do you know who he is?”
Anyone with information should call British Transport Police on 0800 40 50 40 or ring Crimestoppers, anonymously, on 0800 555 111. In all calls quote log PSUB/B13 of 9/4/15.