On 2022 September 26, NASA's Double Asteroid Redirection Test (DART) successfully hit Dimorphos, the smaller companion of the binary system formed with the asteroid (65803) Didymos. Both the binary system and the impact event were imaged by the Light Italian Cubesat for Imaging of Asteroids, detached from DART 15 days before the impact. Images from the onboard LUKE red, green, and blue camera together with ground-based observations enabled the reconstruction of Didymos's brightness phase curve, with phase angles ranging from 2.35° to 107.7°. The opposition effect regime was studied using the exponential-linear equation, the “Shevchenko” function and the linear-by-parts model while the IAU-official HG1G2 magnitude system was applied to the full phase curve. The opposition effect indicates an unusual asteroid surface for an S type, with characteristics similar to M-type asteroids. While the HG1G2 parameters from the full phase curve place Didymos well among asteroids of the taxonomic C complex. Didymos’s phase curve parameters when compared to near-Earth asteroids are very close to the Q type (1862) Apollo, indicating possible depletion of fine submicrometric grains through resurfacing. Didymos's geometric albedo (0.15 ± 0.01) is reported to be 30%–45% smaller than the average geometric albedo for near-Earth S types (0.26 ± 0.04). We propose that Didymos might be an LL ordinary chondrite analog containing albedo-suppressing, shock-darkened/impact melt minerals that have undergone resurfacing processes in the past. A comparison with meteorites indicates that, less likely, Didymos could also contain materials analog to carbon-bearing brecciated L3 ordinary chondrites.