Equation 677 Database

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Magma 5064faf2efb9…

magma 5064faf2efb9
Size
61
Isomorphism class hash
5064faf2efb9ff902dfa8cacade7196503afd65cf5a836aa68b757cc0ba355f2
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 21:19:36
Display reorder
0,1,52,42,17,34,3,36,20,27,45,5,12,8,18,22,11,9,51,6,25,58,10,59,46,21,14,26,39,35,50,33,44,31,13,19,57,24,54,43,37,49,2,4,32,7,23,16,48,28,56,38,29,30,53,41,47,55,60,40,15 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 23:52:21 · history