Allison Transmission Holdings Inc. shares rose in their trading debut Thursday after the Indianapolis-based manufacturer raised more than sought in its initial public offering.

After falling in early trading, shares rose 1.7 percent, to close at $23.40 each, giving Allison a market value of about $4.2 billion.

The company on Wednesday raised $600 million in the IPO, selling 26.1 million shares for $23 each after offering 21.7 million shares at $22 to $24.

The IPO price valued Allison’s stock at $4.2 billion, or almost triple the equity value when Carlyle Group LP and Onex Corp. bought the business from the predecessor of General Motors Co. in 2007. It also makes Allison twice as expensive as Delphi Automotive Plc and Remy International Inc., two other former units of the automaker, according to data compiled by Bloomberg.

Including net debt, Allison’s IPO price valued the company at $7.2 billion, or about 11 times last year’s earnings before interest, taxes, depreciation and amortization. Delphi, the car-parts maker that went public last year, had an enterprise value- to-EBITDA multiple of about 5.5 as of March 13, data compiled by Bloomberg show. Remy, the former GM unit that exited bankruptcy in 2007, had an enterprise value of about 5.4 times EBITDA, the data indicate.

The shares are trading on the New York Stock Exchange under the symbol ALSN. The company has benefited from a surge in truck sales, reporting net income of $103 million last year after returning to profit in 2010. Allison got 34 percent of its 2011 revenue, or $727 million, from parts for on-highway vehicles in North America, Allison’s IPO filing showed.

So far, Allison’s market share among interstate hauling trucks has remained small because manual transmissions get better mileage. Frequent starts and stops of city driving make automatic transmissions popular for garbage and delivery trucks and other work vehicles.

Allison sees growth potential for short haul tractor-trailers used on highways and in cities, CEO Lawrence Dewey said in an interview. A new transmission is being tested with more than 55 fleets, including Wal-Mart Stores Inc., FedEx Corp., and United Parcel Service Inc., he said.

The transmission should be available next year, he said. Allison also has had interest from fleet operators in Europe and Asia, where penetration of automatic transmissions is lower than in North America.

“We think the value proposition will be very attractive,” Dewey said. “Certainly that’s been the feedback.”

Carlyle and Onex bought Allison at the tail end of a private-equity buying spree from 2005 to 2007, when about $1.6 trillion in leveraged buyouts were completed, according to Preqin Ltd., a London-based research firm. The two private-equity firms received all of the proceeds from the offering.

GM sold Allison, which it acquired in 1929, to raise cash. The automaker reorganized under a U.S.-backed bankruptcy in 2009.

Allison traces its roots to Jim Allison, who was a co-founder of Indianapolis Motor Speedway, home of the Indianapolis 500 auto race, a track built to test race car parts. GM bought the company in 1929 after Allison’s death.