Equation 677 Database

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Magma fe5421e4e8a3…

magma fe5421e4e8a3
Size
61
Isomorphism class hash
fe5421e4e8a32d9111ae08268aa2e72179e111b4ca7abd5ee52522e4f3f4ee2e
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 21:19:37
Display reorder
0,1,42,6,2,34,20,51,9,52,54,4,16,60,14,33,19,13,40,31,37,47,53,46,49,18,15,27,24,50,28,25,11,57,22,30,5,41,35,58,26,38,21,7,23,32,45,3,48,39,56,36,8,44,29,59,55,43,10,17,12 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