We present Perm, a learned parametric representation of human 3D hair designed to facilitate various hair-related applications. Unlike previous work that jointly models the global hair structure and local curl patterns, we propose to disentangle them using a PCA-based strand representation in the frequency domain, thereby allowing more precise editing and output control. Specifically, we leverage our strand representation to fit and decompose hair geometry textures into low- to high-frequency hair structures, termed guide textures and residual textures, respectively. These decomposed textures are later parameterized with different generative models, emulating common stages in the hair grooming process. We conduct extensive experiments to validate the architecture design of Perm, and finally deploy the trained model as a generic prior to solve task-agnostic problems, further showcasing its flexibility and superiority in tasks such as single-view hair reconstruction, hairstyle editing, and hair-conditioned image generation. More details can be found on our project page: https://cs.yale.edu/homes/che/projects/perm/.