The Automorphism Group of the Canonical Bipartite Double Cover of the Line Graph of the Petersen Graph

We determine the full automorphism group of the connected bipartite quartic graph X = KC(L(P)), the canonical bipartite double cover of the line graph of the Petersen graph. The canonical covering construction displays a subgroup isomorphic to S5 x C2, but this subgroup is only the stabilizer of one selected quotient frame. An independent homogeneous-space realization identifies X as the unique connected member of the certified quartic self-paired orbital census for the action of S5 on S5/V4,even. The normalizer quotient N_S5(V4,even) / V4,even ~= S3 acts through the centralizer of the degree-thirty coset action. Certified uniqueness of the connected quartic orbital forces this complementary S3 to preserve the graph. Exact automorphism enumeration then gives Aut(X) ~= S5 x S3. The three involutions of the complementary S3 yield a three-member automorphism orbit of regular two-fold quotient frames. Each quotient is isomorphic to L(P), each frame stabilizer is isomorphic to S5 x C2, and the three pair partitions are pairwise block-disjoint, containing forty-five distinct unordered vertex pairs in total. The paper also places X in the four-element S5-fixed binary cohomology square over L(P), where X is the all-one cover class. Exact computational certificates support the quartic orbital census, the cover-orbital identification, the full automorphism-group order, the quotient-frame orbit, and the invariant cohomology calculation.