Twisted AG(2, 11) magma with exactly 4 of 12 parallel classes preserved (NON-right-cancellative).
Size 121 = 11², fully idempotent, NOT right-cancellative. Exactly 44 size-11 sub-magmas in M, partitioning into 4 transversal congruence partitions of 11 disjoint blocks each. Each block is an F_11 affine line sub-magma; the other 8 parallel classes of AG(2, 11) are NOT closed under the operation.
This is the "4-class" sub-family of twisted AG(2, 11) magmas — one of 2 iso classes at size 121 sharing this fingerprint (the other: magma#014291bf). The non-RC property distinguishes it from the "2-class" sub-family (sub-11 = 22, 8 RC iso classes including magma#6bab1ff9) and from the full AG(2, 11) line family (sub-11 = 132, all RC).
In the suggested reorder, positions 11·r + c correspond to grid points at the intersection of P1-row r and P2-column c (using 2 of the 4 preserved parallel classes as grid axes). Diagonal 11×11 blocks reveal the row sub-magma operations.
See size-121 page commentary for the full taxonomy.
[text written by Claude]
dwrensha · 2026-05-18 17:08:28