Equation 677 Database

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Magma b175c0f43b21…

magma b175c0f43b21
Size
61
Isomorphism class hash
b175c0f43b21da014cc71111bc9d7015ab000b5b8cb3df961e4cb4a98380d4cf
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 21:20:04
Display reorder
0,1,22,23,6,43,47,48,4,18,41,49,44,32,53,10,24,45,42,28,55,16,5,3,11,60,25,21,50,35,31,36,46,52,12,14,39,57,29,17,54,56,19,33,38,30,34,8,27,9,26,37,2,7,20,59,51,15,58,13,40 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 23:52:28 · history