We construct an explicit nontrivial finite p-group G of odd order with p = 1009 and |G| = |Aut(G)| = 1009^52359, giving an affirmative answer to D. MacHale’s problem 16.63 in the Kourovka Notebook. Here Aut(G) is the full automorphism group.

The group is obtained by the finite Baker–Campbell–Hausdorff construction from an explicitly specified rank-31 Lie ring modulo 1009^1689. Its nilpotency class is at most 846 < 1009. An asymmetric lattice and a rigid finite-field flag force every finite Lie-ring automorphism into an integral logarithm–exponential domain. A precision-preserving bijection then identifies the full automorphism set with the kernel of an exact derivation matrix. Its rank is 931, its nullity is 30, and its nonzero 1009-primary Smith valuations have multiplicities 87, 55, 758, 6, and 25 at valuations 0, 1, 2, 3, and 4. Their sum is 1689. The finite Lazard correspondence preserves the full automorphism group and completes the group-theoretic conclusion.

This record contains the unrefereed preprint and its focused companion archive: editable LaTeX, the explicit group specification, exact certificates, verification software, computational logs, and scoped AI audit reports. The underlying Lie-algebra template is credited to Omirov and Ruan, arXiv:2605.04602v1, Theorem 4.8. Version 1.1.0 adds artifact citations, two mathematical clarifications, and publication-disclosure improvements; the mathematical construction and computational data are unchanged.

The construction, proof development, and initial verification software were generated using ChatGPT-6 Astra Pro. Separate Codex sessions performed additional AI-assisted reviews and exact computational checks. All checks described in the accompanying audits were completed, with no unresolved error identified within their stated scope. These checks do not constitute external human peer review or proof-assistant formalization. No minimality claim is made for the prime or group order.