Every fingering that fits a hand
102x
open · no 5
1023
open · no 5
1323
moderate
x889
moderate · barre · no 5
What is true of it
A♭7 is A♭, C, E♭ and G♭ — 1, 3, 5 and b7 counted from A♭.
On an instrument that cannot reach all 4, the 5 goes first, in that order.
The easiest of the 4 fingerings below is 102x: 2 fingers, held at the 1st fret.
2 of them use open strings, which is what makes a shape quiet to change to.
1 of the 4 need a barre.
It leaves out the 5. 4 strings cannot carry 4 notes, and the 5 is the one this chord can lose without changing what it is.
1 string stays silent.
Where its notes are on the neck
The brass dots are A♭, the root. Everything else is a chord tone with its degree printed in it.
With a different note underneath
A♭7/C
5646
A♭7/E♭
8889
A♭7/G♭
bcbb
An inversion is the same chord with a different note lowest. The name changes to a slash name because the bass is what a listener hears as the foundation.