Three teenagers who beat a homeless man to death following a dare have been ordered to be detained.

Brothers Connor Doran, 17, and Brandon Doran, 14, and their friend Simon Evans, also 14, attacked Kevin Bennett, 53, as he slept rough outside a supermarket in Liverpool.

During their trial at Liverpool crown court, the jury was told that Connor had goaded Evans by saying: "I bet you haven't got it in you to do him in."

Evans later told his friend: "I started kicking him, I booted him and now he's dead," the court heard. Brandon Doran stood lookout as the attack took place, the prosecution said.

The three boys, who all denied murder, were found guilty on 26 February following a four-week trial.

Passing sentence on Monday, judge Clement Goldstone QC, the recorder of Liverpool, said: "I think it is a desperately sad reflection on this society that each of you was party to serious violence purely for the sake of it."

Kevin Bennett, who died in hospital six days after the beating. Photograph: PA

Connor Doran, labelled by Goldstone as the leader of the pack, was sentenced to a minimum of 12 years, Evans was ordered to serve at least eight years and Brandon Doran received six years.

The brothers' mother, Linda Doran, 42, was jailed for 30 months after being convicted of perverting the course of justice by providing false alibis for her sons.

Last October, her eldest son, Ryan, 23, was convicted of murder and jailed for life after he attacked a complete stranger with a bottle in a takeaway.

The judge told the mother: "You have another son who is serving life for murder. There are not many parents who have that sort of personal agony to bear. But then again, not that many mothers would have shown themselves to be either so unwilling or unable to shoulder the responsibility of motherhood as you have."

During the trial, Doran's second son, Jordan, 21, was held in contempt of court after being caught using a mobile phone to take photographs in the courtroom.

Bennett died in hospital six days after the beating in the early hours of 17 August last year. The victim, described by the prosecution as "vulnerable" and a heavy drinker, suffered a fractured eye socket, a collapsed lung and a broken ribcage which detached from his chest.

He died in hospital from blood poisoning after an infection set in, causing his organs to fail, the postmortem found.

The three boys were responsible for a group attack, the prosecutor Alan Conrad QC told the jury. Bennett had done nothing to deserve such violence, he said. "Those who attacked him were much younger and more agile than he was – very young indeed."

Bennett had been in the pub from 11am on 16 August and had consumed between 10 and 12 cans of lager. He left just after midnight with a white carrier bag laden with more cans of beer and settled down for the night behind an Iceland store on nearby County Road, Walton. It was there that he was discovered by Iceland staff arriving for work at 7am the next day.