Equation 677 Database

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Magma ebea3e11487c…

magma ebea3e11487c
Size
61
Isomorphism class hash
ebea3e11487c6655e73ecb3497d2a5e85d65a8de229650fc24ef9501d9991759
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 21:20:36
Display reorder
0,1,7,23,8,60,53,35,59,10,54,21,16,32,3,29,48,50,9,55,4,49,46,57,41,45,27,36,25,19,51,42,17,20,24,33,31,39,28,6,44,13,58,22,30,34,5,18,43,56,2,40,15,12,11,52,26,14,38,47,37 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 23:52:37 · history