Equation 677 Database

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Magma c27cf8c7f887…

magma c27cf8c7f887
Size
61
Isomorphism class hash
c27cf8c7f8876d33337d813add63a796ec747bb90458db90feaa0653d9006583
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 21:20:41
Display reorder
0,1,18,31,5,21,19,47,43,55,15,28,42,6,23,51,48,12,3,10,13,34,14,57,53,8,27,17,33,44,59,35,7,60,20,58,26,29,25,41,38,16,2,37,32,39,56,40,50,24,4,22,52,54,46,9,36,49,30,11,45 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 23:52:38 · history