Equation 677 Database

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Magma 30b5fef87507…

magma 30b5fef87507
Size
725
Isomorphism class hash
30b5fef8750700c943eb44536e7d23266ce449c7369761efb39df1cb6b488d6c
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Submitted by
omegaestable
Submitted at
2026-08-02 18:22:29
Display reorder
722,290,301,284,299,291,306,288,289,294,307,302,285,281,304,283,297,303,293,298,295,296,305,286,287,280,300,292,282,723,617,634,630,616,618,639,631,632,627,640,642,628,625,620,641,635,643,622,633,623,624,638,636,626,621,637,619,629,708,174,183,171,187,168,192,178,176,177,194,184,175,169,188,182,195,186,179,189,172,170,190,185,180,193,191,181,173,711,226,238,227,242,224,243,230,228,233,245,249,231,234,239,247,250,251,235,244,225,236,241,240,232,248,246,237,229,716,206,216,205,220,203,223,197,208,196,211,215,209,200,219,213,214,217,199,222,204,202,221,218,198,212,210,201,207,707,491,500,490,501,481,479,485,489,492,497,480,495,484,503,478,502,499,486,496,493,487,483,482,488,476,498,477,494,715,536,558,533,548,545,553,540,538,539,555,559,537,544,549,557,556,547,541,550,534,532,551,546,542,554,552,543,535,724,13,15,5,14,3,22,9,11,4,20,23,2,12,26,25,27,21,6,19,8,10,24,17,7,18,16,0,1,717,406,408,396,410,395,417,399,400,402,418,393,403,397,415,419,413,414,401,412,405,392,416,411,398,407,409,404,394,705,64,74,57,76,59,71,56,69,58,81,70,60,62,82,73,79,75,61,78,65,66,83,72,68,77,80,63,67,703,326,335,330,316,313,325,311,332,309,324,328,312,310,323,322,314,315,317,334,320,331,321,318,329,319,327,308,333,709,647,658,650,648,665,645,656,651,654,661,670,652,671,663,657,669,646,667,664,644,666,649,660,668,655,659,653,662,712,424,440,426,439,427,446,422,423,420,447,442,421,432,444,441,438,443,429,435,425,431,445,437,433,436,434,428,430,719,370,389,377,379,375,388,374,372,369,390,380,367,365,384,378,387,382,371,381,368,366,386,391,376,385,383,373,364,718,567,580,572,577,573,582,576,560,564,583,585,574,570,587,584,578,586,562,581,568,569,563,561,575,579,566,565,571,704,694,692,696,687,677,693,697,689,695,673,675,686,691,682,685,698,674,684,699,679,683,680,678,676,688,681,672,690,702,345,358,355,362,353,342,348,343,354,340,337,352,344,339,338,363,341,356,357,347,349,336,360,346,361,359,351,350,721,268,253,263,274,264,272,256,258,267,252,275,262,266,276,273,271,255,260,254,259,261,270,277,257,278,279,269,265,720,141,157,145,161,143,158,144,142,151,160,164,149,148,154,162,155,166,153,163,152,150,156,159,146,167,165,140,147,714,513,523,517,529,516,507,512,510,511,525,509,519,515,522,527,530,528,520,526,521,514,524,504,518,531,508,505,506,710,36,50,39,54,37,53,40,38,31,55,45,28,30,49,43,48,47,33,42,34,32,51,52,29,46,44,35,41,706,88,98,93,110,94,105,89,86,84,107,100,97,87,106,103,101,104,96,111,95,85,108,102,91,109,99,90,92,701,602,593,603,614,596,594,599,600,601,612,608,605,598,609,606,610,592,590,607,597,595,611,615,604,613,591,589,588,700,118,128,124,129,113,126,114,115,120,132,136,121,116,135,134,139,133,119,127,117,112,131,137,123,138,130,125,122,713,460,466,455,470,453,463,450,448,461,465,469,459,454,473,467,464,471,449,472,458,456,475,468,452,462,474,451,457 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Operation: componentwise direct product of magma#d732efd172ca (order 25, the sporadic non-right-cancellative "half-AG(2,5)" solution) and magma#9f34fd7dead4 (order 29, Tao Type II 2-piece translation-invariant). Provenance: melvyn lab session 44, problem magma-677-255. Invariants: all 725 elements idempotent, so the l-profile is 1^725; rows are permutations but columns are not, so this is E677 and NOT a quasigroup - the class that is the only possible shape of a finite E677 counterexample to E255; E255 holds at every point; the translation group is transitive.

last edited by omegaestable at 2026-08-02 18:24:16 · history