Equation 677 Database

← all  ·  ← by size  ·  ← size 61

Magma e1aef7169f26…

magma e1aef7169f26
Size
61
Isomorphism class hash
e1aef7169f2675f0eba4c0ac28de86191fef20e49964d073021640400e402995
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 21:20:25
Display reorder
0,1,44,7,22,33,18,50,56,29,32,40,60,14,48,39,53,2,24,3,11,17,30,42,15,37,20,27,43,13,41,12,23,45,8,59,4,46,58,52,9,21,54,28,6,19,38,31,57,10,36,26,55,16,34,35,49,51,5,25,47 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 23:52:34 · history