GALÆXI is a GPGPU-enabled extension of FLEXI, a high-order numerical framework for solving PDEs, with a special focus on Computational Fluid Dynamics. GALÆXI is based on the Discontinuous Galerkin Spectral Element Method (DGSEM), which allows for high-order of accuracy and fully unstructured hexahedral meshes. The solver is parallelized very efficiently for large-scale applications using MPI-aware CUDA Fortran and has demonstrated excellent scaling on over 1000 NVIDIA GPUs. Moreover, GALÆXI comes with a capable pre- and postprocessing suite that enables complex simulation setups up to the finished visualization.