What is true of it
G♯13 is G♯, B♯, D♯, F♯, A♯ and E♯ — 1, 3, 5, b7, 9 and 13 counted from G♯.
On an instrument that cannot reach all 6, the 5, 9 and 1 go first, in that order.
No fingering of G♯13 fits a hand on the ukulele: inside four frets, with the strings that sound next to each other and the root underneath, there is nothing to hold.
Where its notes are on the neck
The brass dots are G♯, the root. Everything else is a chord tone with its degree printed in it.
With a different note underneath
G♯13/B♯
5668
G♯13/D♯
8688
G♯13/F♯
x688
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.