Skew braces and Hopf–Galois structures of Heisenberg type

We classify all skew braces of Heisenberg type for a prime number p>3. Furthermore, we determine the automorphism group of each one of these skew braces (as well as their socle and annihilator). Hence, by utilising a link between skew braces and Hopf–Galois theory, we can determine all Hopf–Galois structures of Heisenberg type on Galois field extensions of fields of degree p3.