Equation 677 Database

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Magma 9aee6a691158…

magma 9aee6a691158
Size
61
Isomorphism class hash
9aee6a69115859cdf001ba9bb3af50f19d3f4bc9c1ee9237cc073fc8ee231fa3
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 21:20:01
Display reorder
0,1,22,3,29,24,42,39,30,48,57,58,53,60,18,54,16,33,49,20,25,47,35,56,43,55,19,28,45,14,40,27,50,12,2,4,34,26,13,46,10,8,38,9,59,44,52,17,23,31,37,7,15,11,51,6,21,36,32,41,5 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 23:52:28 · history