Equation 677 Database

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Magma 03b5a3568c5b…

magma 03b5a3568c5b
Size
61
Isomorphism class hash
03b5a3568c5ba89da125a80407e0915e5b7eaffae37f71619b72ab6420fdb676
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 21:19:39
Display reorder
0,1,22,49,47,55,8,25,44,19,16,34,5,13,53,59,36,10,42,11,3,58,9,23,12,51,15,37,35,60,6,43,39,24,40,45,14,21,18,38,29,41,31,46,2,30,52,54,32,4,48,57,28,17,26,56,50,33,7,20,27 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 23:52:22 · history