California’s largest auto insurer, Farmers Insurance Group, said Thursday that it planned to slash jobs at the offices of its newly acquired 21st Century Insurance unit in Woodland Hills.

Los Angeles-based Farmers told employees that it would cut 554 jobs by the end of this year and that the total would reach 750 by the end of 2010.

The Woodland Hills complex, which had been 21st Century’s headquarters until last November, currently has 979 employees, Farmers said. Farmers completed its purchase of 21st Century from troubled insurance giant American International Group Inc. on July 1.

With the merger, Farmers — a traditional insurance company that sells home, auto, life and other insurance products with a network of agents — added 21st Century’s system for selling auto insurance directly to motorists via telephone and the Internet.

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