Equation 677 Database

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Magma b8dc6b887261…

magma b8dc6b887261
Size
61
Isomorphism class hash
b8dc6b8872614b853eebdb68c614577f96303fefda33f88e0122f63c856347dc
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 21:20:38
Display reorder
0,1,34,20,60,31,16,22,28,13,44,37,48,10,8,47,3,11,42,21,29,59,4,35,7,18,49,58,38,9,55,33,56,19,39,15,41,53,43,36,25,46,12,6,50,32,51,17,45,27,24,5,2,26,52,23,30,40,57,14,54 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 23:52:37 · history