Equation 677 Database

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Magma 9ead2b476c2b…

magma 9ead2b476c2b
Size
61
Isomorphism class hash
9ead2b476c2bdd8520f60fd7863ed3cee0eaa181ad5624699f3e603a513b1ea5
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 21:19:44
Display reorder
0,1,20,13,2,14,37,24,17,6,4,35,58,60,8,28,57,11,43,21,52,32,7,30,36,56,9,49,45,46,38,55,47,16,48,18,25,54,42,12,41,44,23,19,15,50,3,33,40,29,26,51,34,39,31,5,22,27,59,10,53 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 23:52:23 · history