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PhatFatI thought it was GLH for "Goes Like Hell"
It was.
But there was the GLHS on top of the GLH. Goes Like Hell - Shelby.
There was the regular Omni GLH, which debuted in '84 with an HO 2.2L I4 with 110hp. Comparable to a Volkswagen GTI of the time.
In '85 the GLH got a turbocharged version of the engine as an option, with 146hp. It wasn't intercooled though.
In '86 Shelby Automobiles got involved. The Shelby GLHS was a GLH with a whole whack of new Shelby parts and complete suspension revision. And more importantly an intercooler for the turbocharger, which made power jump to 175hp. The GLH was "quick", but the GLHS was an absolute monster. 0-60 in 6.5s. Quarter mile in the mid- to high-14s.
May not seem all that impressive today, but a GLHS could proverbially *****slap a similar vintage top-of-the-line Camaro and Mustang, and not all that far behind a Corvette. And the GLHS was built to handle to boot.