Equation 677 Database

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Magma 1a41aeda4f8f…

magma 1a41aeda4f8f
Size
61
Isomorphism class hash
1a41aeda4f8fd79533ccd70ff523114d70a84014a61bb93b72e8eeda04e65e90
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 21:19:46
Display reorder
0,1,32,40,42,39,54,22,31,8,35,38,34,57,20,19,13,55,9,30,21,59,7,56,18,25,45,15,24,47,49,5,10,50,33,52,37,28,16,11,27,44,2,53,26,60,46,29,41,51,48,17,4,14,23,12,58,3,6,36,43 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 23:52:24 · history