Was the insect Gregor turned into in The Metamorphosis a spider or a grasshopper?

I've read this story many times throughout high school and college, and I am almost certain that at no time was the specific insect ever named; however, I am certain that it was not as spider, as that is an arachnid.  I will say this, though, I do remember a brilliant college professor and a lengthy discussion that seemed to lean toward the idea of a cockroach, simply based on the author's description.  If I had to choose one, I would go with that.