Equation 677 Database

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Magma 4706da12746a…

magma 4706da12746a
Size
61
Isomorphism class hash
4706da12746a98bb04f275c62a522a35559c80874bcb2c711ef61d01ef4e7956
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 21:19:50
Display reorder
0,1,13,11,30,53,41,16,17,24,3,44,29,21,43,31,58,60,7,42,27,10,26,15,19,39,59,5,38,2,36,47,32,56,4,46,18,14,33,22,50,12,28,8,40,57,6,25,51,52,54,48,34,49,20,37,35,45,9,55,23 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 23:52:24 · history