By Aidan Lewis and Ahmed Elumami

WADI BEY, Libya, April 13 (Reuters) - Packed into a battered car, a family of nine joined the steady flow of residents fleeing Islamic State's Libyan stronghold of Sirte. They were heading to a nearby town to pick up essentials: cash, medicine and food.

A few kilometres beyond the militant group's zone of control, the family gave an account of life in the city: young men murdered for refusing to pledge allegiance to Islamic State, public beatings for dress violations, property seizures and growing food shortages.

"They're there to occupy the city," said the wife from behind her black veil, as her children glanced nervously from the rear of the vehicle one afternoon in late February. "They're killing, kidnapping and torturing."

Sirte is a city upended. Once given favoured treatment by former leader Muammar Gaddafi, who was born there, it now serves as a Mediterranean base for the most important Islamic State branch outside Syria and Iraq. That has left Western intelligence agencies struggling to figure out how far Islamic State can extend its influence across Libya - and how to stop the group.

Some Libyan and Western officials see Sirte as a foothold for further Islamic State expansion. From there the ultra-hardline Sunni group has ventured east along the coast, edging closer to major oil fields. It now controls a thin strip along about 250 km (155 miles) of Libya's central coastline.

Though Islamic State's manpower in Libya is uncertain, membership has been growing. Western intelligence agencies and the U.N. estimate its fighting force, which includes a growing number of foreigners, at between 3,000 and 6,000. "Their dream is to control the oil fields in the east and expand to the west to Tripoli and Misrata," said Mahmoud Zagal, head of the Misrata military operations room for local forces opposed to Islamic State.

But much still hangs in the balance, and ISIS may struggle to control large swathes of the country. General David M. Rodriguez, head of U.S. Africa Command, told a news briefing in Washington on April 8 that it will be difficult for Islamic State to seize huge swathes of Libya "because they don't have the home-grown people that know as much about Libya like they did in Iraq and Syria." Libyans, he said, "don't like ... external influences."

"PEOPLE ARE AFRAID"

Islamic State entrenched itself in Sirte by early 2015. The city had been neglected by Libya's main factions since Gaddafi was dragged from a drainpipe and shot there in 2011.

Sirte mayor Mukhtar Khalifa al-Maadani, who left the city in August last year as Islamic State escalated its crackdowns, said the group cleverly exploited the city's existing rifts. "Sirte is a mix of many tribes, and they took advantage of this ... They have individuals from every tribe in Sirte supporting them and they used this to tear apart its social structure."

The group has built the trappings of a rudimentary state in the city. It collects taxes, directs religious education, broadcasts its messages on radio, and enforces its rule with increasing brutality, Libyan officials say. It also makes money by kidnapping, selling stolen property, smuggling drugs and possibly trafficking migrants.

One woman who left the city in January, five months after her husband was abducted by Islamic State fighters, described how men accused of espionage have been crucified, with their bodies strung to poles for days; how suspected thieves have their hands chopped off in public; and how women are whipped when caught flouting dress regulations by female members of Islamic State police.

"People do not fight back because they are afraid," said the woman, who fled when her teenage son was asked to report on people smoking or drinking alcohol.

While teenage girls are made to wear full-face veils and black robes, boys have been conscripted as Islamic State "cubs." A recent U.N. report cited the cases of two recruits, aged 10 and 14, who said they had been seized from their families by Islamic State then subjected to weeks of religious and military training, forced to watch videos of beheadings and sexually abused.

In Sirte and beyond, recruits, including some migrants, have been offered salaries many times greater than the average wage, as well as enticements such as cars and brides, Libyan officials and residents say.

In Iraq the group drew heavily on former members of Saddam Hussein's regime. In Libya it has used former Gaddafi-era operatives, but to a lesser extent.

"The organisation has its own presence," said Abdulraouf Kara, the head of Tripoli's Special Deterrence Force, a brigade of more than 600 men whose focus has shifted from anti-vice operations to rooting out Islamic State militants. "Some individuals who support Gaddafi joined to take revenge. But we can't say it's an organisation based on Gaddafi's followers."

FOREIGN FIGHTERS?

Islamic State's advance in Libya has been far from smooth. The group has to compete with a complex web of established armed factions, in a country without the Sunni-Shi'ite divide that Islamic State has exploited in Iraq and Syria.

It has suffered military setbacks. In the eastern city of Benghazi, it recently lost territory to the army, and in western Sabratha, it was chased out by local brigades in the wake of a U.S. air strike in February.

Sirte residents and Libyan officials say Islamic State is increasingly dominated by foreign fighters, a possible sign of a lack of traction amongst locals.

In a rare admission of weakness, Abdul Qadr al-Najdi, the Islamic State leader in Libya, said last month that the group had found it hard to replicate its conquest of Sirte. "The number of factions and their disputes are one of the reasons of failure and the rest of the cities in Libya are a living example of this," he said in an interview with Islamic State newspaper al-Naba.

Below the surface in Sirte, opposition festers. Last August, residents took up arms after an imam was killed for refusing to pledge allegiance to Islamic State. Dozens were killed and the revolt was crushed. "Everyone left in Sirte is opposed to Islamic State but they can't do anything to resist them," said one resident who had travelled to Misrata to get medical treatment for his father.

Libya's ability to fight Islamic State has depended largely on the country's two main loose military alliances, which are aligned with rival power bases, one in the west and one in the east.

The groups occasionally announce plans to tackle Islamic State, but action is haphazard. In Libya's "oil crescent" east of Sirte, the Petroleum Facilities Guard has fended off attacks while complaining that the eastern army, to which it was allied in the past, was providing no support.

Kara, the Deterrence Force leader in Tripoli, complained that armed groups that back the government in Tripoli try to protect Islamic State suspects. "When we try to arrest them we are told that they are 'thuwwar'," he said, using the term for anti-Gaddafi revolutionaries. "We are asked to release them every day."

Western powers hope the new U.N.-backed unity government, whose leaders arrived in Tripoli last month, will help by drawing Libyan brigades together and winning longer-term international help.

"If we do manage to create this national unity government, there won't a Libyan army as we'd like it," said a French defence ministry official. "But there are a number of forces, which, if they worked together, would have enough strength to hit (Islamic State)." (Additional reporting by John Irish in Paris; Edited by Simon Robinson and Richard Woods)