Equation 677 Database

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Magma 1bdfe90eff00…

magma 1bdfe90eff00
Size
61
Isomorphism class hash
1bdfe90eff0047ea6200fee85ed2eb02a5b13c73d44937de4d05b3d7f4e78e69
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 21:20:29
Display reorder
0,1,45,26,20,22,43,35,19,27,10,32,55,13,24,44,3,25,30,54,23,52,50,4,36,58,49,6,33,34,8,53,59,14,56,42,11,17,29,12,2,9,40,51,60,5,16,15,21,28,38,47,31,46,41,37,18,57,39,48,7 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 23:52:35 · history