- SmallGroup(32,43) is indeed the group we're talking about here:
https://groupprops.subwiki.org/wiki/Holomorph_of_Z8
It's called the "holomorph" of ℤ/8 because it's the semidirect product of ℤ/8 and its automorphism group (which as Greg checked is the multiplicative group of ℤ/8).