The Automorphism Group of AT4val[60, 6]

We determine the full automorphism group of the connected quartic sixty-vertex graph AT4val[60, 6], denoted G60. The graph carries a canonical fixed-point-free deck involution whose thirty two-element orbits define a two-fold quotient G60 -> G30. The quotient automorphism group has order 240 and is isomorphic to S5 x C2. Every quotient automorphism has exactly two lifts to G60, producing a subgroup of order 480. An independent exhaustive enumeration performed directly on the exact native sixty-vertex graph also returns exactly 480 automorphisms. The enumerated native group agrees element-for-element with the lifted group. Every native automorphism preserves the canonical fiber partition and centralizes the deck involution. The internal group structure is determined exactly. The center is C2, the derived subgroup is A5 x C2, the second derived subgroup is A5, and the abelianization is C2 x C2. The full automorphism group is identified as the fiber product Aut(G60) ~= S5 xC2 D8, where the sign character of S5 is matched with a quotient character of D8 whose kernel is a Klein four subgroup. An explicit bijection between the 480 native automorphisms and the 480 elements of the fiber-product model is constructed, and all 230400 ordered products are verified. The paper includes exact machine-readable certificates, deterministic encodings, reproducibility workers, and explicit claim boundaries.