Equation 677 Database

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Magma b8ecd8543537…

magma b8ecd8543537
Size
61
Isomorphism class hash
b8ecd85435377cb9d2fecfd7bc1ebb7a97553c424d83c7fba1b6a66479a59321
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 21:20:08
Display reorder
0,1,19,25,29,20,15,9,34,4,31,6,38,10,57,28,14,18,60,27,32,11,2,39,52,13,37,35,21,54,22,40,55,49,50,16,24,23,45,17,26,42,59,41,44,30,3,5,8,47,43,48,46,36,12,51,33,56,58,53,7 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 23:52:30 · history