Equation 677 Database

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Magma 4689cfed4bb4…

magma 4689cfed4bb4
Size
61
Isomorphism class hash
4689cfed4bb4bc23cd30c27b2540306efe0b80bcdcaf19a20e54fb619ff0c5fe
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 21:19:33
Display reorder
0,1,20,45,10,46,50,3,11,41,48,30,42,13,23,15,4,33,9,32,51,39,16,53,37,40,24,7,44,27,43,56,47,17,55,5,6,36,14,29,8,18,60,52,49,21,34,25,19,54,59,57,12,2,38,31,35,58,22,26,28 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Size-61 magma encoding a Steiner system S(2, 5, 61). Every pair of distinct elements lies in exactly one 5-element sub-magma; the 183 = C(61,2)/C(5,2) such sub-magmas form the blocks of the Steiner system. Each block is a copy of the 5-element linear magma F_5(2,4). Each element lies in exactly r = (61-1)/4 = 15 blocks. The full magma is a quasigroup (LC + RC) with all 61 elements idempotent. R_x has uniform cycle type (1 + 15·4) and L_x has uniform cycle type (1 + 30·2). The database has many distinct iso classes of Steiner S(2,5,61) 677 magmas — they share these combinatorial properties but realize different non-isomorphic block-incidence structures.

last edited by dwrensha at 2026-04-29 23:52:20 · history