On plane quartics with a Galois invariant Cayley octad

We describe a construction of plane quartics with prescribed Galois operation on the 28 bitangents, in the particular case of a Galois invariant Cayley octad. As an application, we solve the inverse Galois problem for degree two del Pezzo surfaces in the corresponding particular case.
Comment: arXiv admin note: substantial text overlap with arXiv:1708.00071