Fortress Investment Group, the first U.S. hedge fund to file for an IPO, wants to raise up to $634 million in its upcoming offering.

The New York hedge fund and private equity firm plans to offer 34.2 million shares at a range of $16.50 to $18.50, according to a regulatory filing. In November, Fortress made a bit of history when it filed for an initial public offering.

Fortress oversees $29.7 billion in assets, making it one of the largest hedge-fund and private-equity managers. Shares will trade on the New York Stock Exchange under the symbol FIG and use the name Fortress Operating Group.

Other U.S. hedges are closely watching the Fortress IPO to see how it's received by investors. Many believe that other hedge funds will soon follow with their own IPOs, if shares of Fortress make a strong debut.

A month after filing for the IPO, Japan's Nomura ( NMR) investment bank announced it was buying a 15% equity stake in Fortress for $888 million. The deal recently closed.

After the offering, the five principals at Fortress -- Peter Briger, Wesley Edens, Robert Kauffman, Randal Nardone and Michael Novogratz -- will own 77.7% of the total combined voting power of the firm's Class A and Class B shares.

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