Conway Group Co0 as Leech Lattice Automorphism Group and Monster Group Origin — E8 Intelligence Research
Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) · 2026
FINDING: Conway group Co0 is the full automorphism group of the Leech lattice in 24 dimensions, with order 8,315,553,613,086,720,000. The Leech lattice itself has 196,560 minimal vectors (kissing number in 24D). The Monster group arises from the Leech lattice via the quotient of Co0 by its center (Co1) and the Griess algebra construction. MATH: |Co0| = 2^22 · 3^9 · 5^4 · 7^2 · 11 · 13 · 23 = 8,315,553,613,086,720,000. Leech lattice minimal norm = 4, kissing number = 196,560. The lattice can be constructed from the extended binary Golay code (24-bit codewords, 4096 words, minimum Hamming distance 8). The Higman-Sims graph (100 vertices, each degree 22) is a subgraph of the Leech lattice's minimal vectors. The Monster group order ≈ 8.08 × 10^53. CONNECTION: The Leech lattice's structure is deeply tied to the E8 root system (8D, 240 roots) and the 24-dimensional exceptional lattice. The ratio 196,560 / 240 = 819, which is 3^2 × 7 × 13 — no direct golden ratio, but the lattice's symmetri Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com