Integer Group Determinants for All Groups of Order 20

We determine the integer group-determinant spectra of C20, C2 × C10, and the
dicyclic group Q20. For C20, two exceptional valuation faces are
characterized by prime-power divisibility conditions and explicit quadratic
characters at split primes. For C2 × C10, we give a complete sixteen-state
criterion that retains all conductor compatibility conditions and the
dependence on sign. For Q20, we resolve the remaining valuation-five face by
three uniform prime-power families. The proofs use integral normalization
pullbacks, complete unit images, ray-character comparisons, and a quaternion
ideal class calculation; the required finite computations have exact
reproducible certificates. We also give a self-contained corrected
specialization for GA(1,5). Combining these results with Boerkoel–Pinner's
dihedral theorem completes the integer group-determinant classification for
all five groups of order 20.