Officers have appealed for help from residents of the Toryglen area of the city who they say may hold vital clues to the attackers' identities.
The woman, aged 33, was targeted at the entrance to flats in Edinbeg Avenue, close to a main police station, after she visited friends in the early hours of Saturday morning.
Police have stepped up patrols since the attack in an attempt to allay the fears of people living in the area.
Local councillor Mhairi Hunter said the attack had shocked the local community.
She added: "This is obviously a horrific incident and extremely worrying for local people.
"I would urge anyone who knows anything to get in touch with police. This is not the kind of place you would expect this to happen. It's a quiet area."
One woman who lives nearby, said: "We never get any trouble here. It's usually so quiet."
Police said the attack happened after one man got out of a car, possibly a white or silver BMW, and forced the woman into the close doorway.
Two other men who were also believed to be in the vehicle then joined in the rape which happened between midnight and 3am on Saturday.
The gang fled and the victim managed to make her way home before raising the alarm the following day.
Detectives said that she has been left "extremely distressed" by her ordeal and is being supported by her family and specially trained officers.
The three suspects are Asian and in their 20s, and wore dark clothing. Police are carrying out door-to-door inquiries in the area.
Chief Inspector Carol McGuire said: "People may have heard something that they didn't think was important at the time.
"However, I would now ask them to come forward and contact police.
"I would like to reassure the public that we have and will continue to have extra uniform patrols in the area.
"A crime of this nature is rare in what is a tight-knit community."