Equation 677 Database

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Magma 3f913a91790e…

magma 3f913a91790e
Size
61
Isomorphism class hash
3f913a91790e319928103cd329fba1403347104b9e8bd1f4c83e132299d253c8
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 21:19:55
Display reorder
0,1,12,26,9,4,24,57,60,31,7,53,15,52,19,59,28,3,18,22,20,33,49,43,58,29,46,23,50,47,8,44,51,27,14,6,21,41,54,35,16,37,34,40,32,10,25,42,5,13,2,55,39,36,48,17,45,56,30,11,38 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 23:52:26 · history