Equation 677 Database

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Magma 8b9a92d13745…

magma 8b9a92d13745
Size
61
Isomorphism class hash
8b9a92d13745d7e076940966d071d559d96dce4e031aa2ebb2424c447087c978
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
yes
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 21:20:34
Display reorder
0,1,6,24,18,48,19,32,54,27,23,25,43,10,4,21,8,42,44,50,58,37,53,45,59,39,34,7,11,33,28,57,38,22,31,41,16,15,49,20,56,60,36,40,55,2,26,47,13,46,29,30,3,51,35,9,52,14,12,17,5 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 23:52:36 · history