Equation 677 Database

← all  ·  ← by size  ·  ← size 61

Magma f3c3816472ba…

magma f3c3816472ba
Size
61
Isomorphism class hash
f3c3816472baadd25245de7e6c90a2fddbbdeba139b7d0e689fa8bb84bd183b0
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 21:19:53
Display reorder
0,1,32,23,56,15,26,20,11,53,18,7,41,55,5,42,34,31,16,51,17,21,35,37,13,28,6,60,43,48,10,44,22,52,29,59,50,57,54,14,12,36,8,9,58,47,3,38,19,2,25,46,39,4,40,30,45,49,24,33,27 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 23:52:25 · history