Equation 677 Database

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Magma 343090d1aa23…

magma 343090d1aa23
Size
61
Isomorphism class hash
343090d1aa23a5ec1732c81bd3a2921ef36f3db43b2121d0d14767fc3f3fa179
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 21:20:18
Display reorder
0,1,22,43,60,18,44,41,19,49,11,27,6,52,53,9,2,55,38,42,17,12,21,29,47,28,36,15,26,54,56,7,14,4,24,51,23,57,46,25,34,10,50,30,20,39,45,37,8,35,33,5,3,32,58,40,16,31,13,48,59 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 23:52:32 · history