Equation 677 Database

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Magma be4a14bddbeb…

magma be4a14bddbeb
Size
61
Isomorphism class hash
be4a14bddbeb724f0ff30600f68bf166b4f710992addfb372353c168fea8611b
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 21:20:23
Display reorder
0,1,18,53,19,51,2,22,46,7,11,28,49,59,23,29,24,36,43,27,14,55,48,12,21,42,45,4,32,52,54,25,10,50,44,60,6,20,57,15,47,5,16,37,38,34,41,9,40,39,56,8,17,3,58,26,33,30,35,13,31 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 23:52:33 · history