Equation 677 Database

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Magma 2e8995b35c2f…

magma 2e8995b35c2f
Size
61
Isomorphism class hash
2e8995b35c2f059349bca5ab1f1c01c7aeb5e4fea64e5c830b6093dcf29f66bb
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 21:20:21
Display reorder
0,1,19,38,24,53,23,11,22,34,25,32,13,58,40,20,52,48,60,7,9,35,37,31,18,55,14,8,54,44,10,45,16,3,57,50,4,2,46,30,56,47,41,43,26,28,39,36,59,27,49,5,12,29,51,6,21,15,17,33,42 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