Equation 677 Database

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Magma 2fd6ffbaec2d…

magma 2fd6ffbaec2d
Size
61
Isomorphism class hash
2fd6ffbaec2d58f44601af97d8f84048b4ec43eaeb681a15caba4123389994fb
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 21:20:32
Display reorder
0,1,31,13,32,8,38,27,14,60,33,18,52,47,6,4,23,12,34,30,43,10,41,7,9,44,22,3,45,50,29,37,28,48,55,15,35,20,57,21,24,5,16,59,56,51,11,25,49,19,46,39,58,42,54,36,2,26,53,17,40 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