Re: which chord is this?
I use that chord alot. Move it up to the ninth fret and let the low E ring open and it's cool, very big sounding E major chord.
As it is, I'd think of it as a C chord with the third (E) in the bass.
It's a great way to voice a C chord if you're playing with a bassplayer who's holding down the Root.
As a C chord, hammer on the third (the E on the A string) and you can start to get into some cool Hendrix, SRV, Curtis Mayfield soul guitar stuff.
Experiment a little...
If the bass player plays an A against it, it'll be a Am7.
Lew