Direct product B31 x F7(b=3): carrier Z31 x Z7, i = 7x+r, (x,r).(y,t) = (5x-4y+1 mod 31, 4r+3t mod 7). Idempotent-free (B31 is), quasigroup, ell-profile {10:31, 30:186}. Provenance: melvyn lab session 27; parents magma#60f580e4 (B31) and the b=3 affine model magma#baf8b55c. Census note: the constant-coefficient difference-indexed cocycle line over B31 with fibre Z7 is coboundary-trivial for both fibre laws (rank 30, nullspace = constants, absorbable since a+b-1 is a unit mod 7) - so unlike the mod-5 M155 line (magma#b9f3f9a0), order 217 admits NO twisted companion of this shape; this product and the (4,1)-side class are the whole constant-coefficient family.
omegaestable · 2026-07-29 16:12:23