Equation 677 Database

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Magma d8c966e4d19c…

magma d8c966e4d19c
Size
61
Isomorphism class hash
d8c966e4d19c1748943024fc8d085234fc62285c3bda30f20419e41ae7326d9a
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 21:20:14
Display reorder
0,1,4,58,7,51,33,55,15,22,60,11,30,44,57,39,13,3,31,20,8,2,27,19,43,26,23,9,6,52,21,10,46,5,12,18,28,40,16,14,48,29,50,54,25,37,47,38,49,41,34,32,42,36,59,56,53,17,24,45,35 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 23:52:31 · history