By Robert MacMillan

NEW YORK, USA - General Motors Corp's survival is in doubt, sales have shrunk and its stock has sunk to levels not seen since the Second World War. Yet the automaker retains its status as one of the powerhouses in the best-known measurement of U.S. stocks, the Dow Jones Industrial Average.

Its market capitalization as of Thursday is $1.8 billion(S$2.7 billion), making it by far the smallest Dow member. Even on a day when the index surged 7%, GM was one of only two of its 30 components to lose ground, dropping 4.2%.

The next smallest, Alcoa , is worth $8.9 billion. Exxon Mobil , the biggest, weighs in at $383.6 billion.

But after 83 consecutive years on the average, there is no sign that News Corp's Dow Jones & Co, which runs the benchmark, has lost faith in General Motors. Indeed, GM was named to a new Dow Jones world index this week.

Dow Jones tries to keep changes to the member roster to a minimum, said John Prestbo, editor and executive director of Dow Jones Indexes. "We think that it not only makes for a better index, but it increases the trust level that people have for the industrial average," he said.

Dow Jones would push out GM if it went bankrupt, or, like insurer American International Group , most of it ended up being owned by the U.S. government in a bailout, he said.

Relevance to the economy - and to U.S. society - is at the heart of what lands a company on the 112-year-old Dow.

Unlike the big U.S. stock markets, there are no minimum stock price or market cap requirements, though the large corporations populating it usually sport robust financials.

Instead, it is more about the size of the role the company plays in the domestic economy and how its financial fortunes provide a barometer for measuring U.S. market health.

To be on the Dow is to telegraph a company's importance far beyond Wall Street trading floors and into the minds of people who otherwise pay scant attention to the world of business.

"When my wife [an occupational therapist] asks me what happened to the stock market, she wants to know what happened to the Dow," said Jay Ritter, a finance professor at the University of Florida in Gainesville.

Robert Thomson, who was picked by News Corp Chief Executive Rupert Murdoch to edit The Wall Street Journal, also part of Dow Jones, is responsible for picking the members, said Prestbo. Thomson was not immediately available for comment.

GM first was listed on the Dow in 1915. Journal editors removed it, as they did more frequently back then, and added it again in 1925. Since then, it has remained. Only U.S. conglomerate General Electric Co , which joined in 1907, has been there longer.

Many investment experts think General Motors should be retired.

"General Motors is no longer relevant as an industrial powerhouse," said Peter Kenny, managing director at Knight Equity Markets in Jersey City, New Jersey.

GM spokesman Tom Wilkinson disputed that notion. The company directly employs 96,000 people and supports over half a million jobs, including those at auto parts suppliers and dealers, Wilkinson said.

"The auto is still probably one of the largest drivers of economic activity in the country and GM is still, by far, the largest part of the US-based auto industry," he said. "GM and other U.S. automakers are still very relevant to the economy."

The Dow has stuck with companies whose finances suffered because their relevance was enduring. One example Prestbo cited was IBM , which has persevered through prolonged tough times. One that didn't, he said, was Eastman Kodak.

"Look at the disappearance of film and the advent of digital photography. It was slow in making that transition," Prestbo said. "Its economic importance as a consumer goods maker had deteriorated because the world was passing it by."

GM's iconic status has diminished in the past 40 years, said Tom Alexander, head of Alexander Trading in Savannah, Georgia. "It's a little bit of a surprise that it's still there," he said, referring to the Index.

Ritter, the finance professor in Florida, explained GM's significance in American society: It was the first stock he bought at age 13 with the money he saved from his newspaper delivery route. That was 1967.

"Eventually I sold it - at a loss."

(Additional reporting by Deepa Seetharaman, Charles Mikolajczak in New York and Poornima Gupta in Detroit, editing by Leslie Gevirtz)