Equation 677 Database

← all  ·  ← by size  ·  ← size 587

Magma dd166ad1cd64…

magma dd166ad1cd64
Size
587
Isomorphism class hash
dd166ad1cd6409ecb3428b7cb29a5534c5e56b356f360d9b9b7f650de73d3ce0
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 586) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 15:15:45
Display reorder
508,467,505,494,504,498,500,487,484,479,489,481,463,486,471,502,460,472,501,470,490,466,482,475,469,457,492,465,474,493,496,509,478,485,507,464,480,456,497,473,491,506,468,488,510,483,495,503,461,477,476,462,499,459,458,572,571,580,586,581,582,573,570,569,565,563,555,564,554,539,527,514,513,511,194,243,135,68,91,359,45,335,329,397,108,311,404,179,323,154,317,276,450,193,245,137,67,90,358,47,334,328,398,110,310,402,178,322,153,316,278,452,195,241,133,69,95,355,43,330,324,400,112,306,405,174,318,152,312,280,454,192,244,136,66,92,357,46,333,327,396,109,309,403,177,321,155,315,277,451,196,242,134,70,93,354,44,331,325,401,113,307,406,175,319,150,313,281,455,197,240,132,71,94,356,42,332,326,399,111,308,407,176,320,151,314,279,453,521,541,538,536,553,552,567,549,534,535,545,550,560,548,551,542,543,537,532,203,181,250,142,73,283,435,35,18,4,416,100,220,260,161,51,368,116,428,202,180,249,141,72,282,437,34,20,3,414,99,219,259,160,53,366,115,426,198,185,248,140,77,287,432,30,16,8,417,98,218,261,156,49,369,117,429,201,182,251,143,74,284,436,33,19,5,415,101,221,258,159,52,367,114,427,199,183,246,138,75,285,434,31,17,6,418,96,216,262,157,50,370,118,430,200,184,247,139,76,286,433,32,15,7,419,97,217,263,158,48,371,119,431,531,519,528,529,518,524,533,547,568,562,561,546,544,523,522,526,520,530,525,422,270,213,352,236,127,304,87,441,390,363,28,412,345,338,389,169,62,382,420,272,215,351,235,126,303,89,443,391,365,27,411,347,340,388,168,61,381,423,274,211,350,237,131,302,85,438,395,360,1,410,342,339,385,173,63,380,421,271,214,353,234,128,305,88,442,392,364,29,413,346,341,387,170,60,383,424,275,212,349,238,129,300,86,440,393,362,0,409,344,337,384,171,64,379,425,273,210,348,239,130,301,84,439,394,361,2,408,343,336,386,172,65,378,512,516,515,517,540,556,566,557,559,558,574,578,577,584,583,585,579,575,576,448,41,291,26,232,103,13,269,167,59,295,123,224,204,191,256,149,81,377,447,40,293,25,231,102,12,268,166,58,294,125,223,206,190,255,148,83,376,446,36,289,21,230,107,11,264,162,54,299,121,225,208,186,254,144,79,373,449,39,292,24,233,104,14,267,165,57,296,124,222,205,189,257,147,82,375,445,37,290,22,228,105,9,265,163,55,297,122,226,209,187,252,145,80,372,444,38,288,23,229,106,10,266,164,56,298,120,227,207,188,253,146,78,374 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 587 = 55 + 4*133, glued along a group-divisible design developed from base blocks under the translations of Z/133; blocks of five points. Points: 0..54 are fixed points; 55 + 133r + a is the point (r, a), r in 0..3, a in Z/133. The fixed points form one group and carry A(55;32,24,0): x*y = 32x + 24y mod 55. For each r and each c in 0..18, the 7 points (r, c + 19i), i in Z/7, form a group and carry A(7;4,1,0) on i: (r, c + 19i)*(r, c + 19j) = (r, c + 19k), k = 4i + 1j mod 7. Two points of different groups multiply in the block through them, which carries A(5;2,4,0) on its points as listed: if the block lists b_0, ..., b_4, then b_i*b_j = b_k with k = 2i + 4j mod 5. Blocks: the translates (r, a) -> (r, a + t), t in Z/133, of the base blocks. Pure base blocks: for each representative B below, each s in {0, 2} and each m in {1, 121, 11}, the block listing (r + s mod 4, m a) for (r, a) in B, in order. Base blocks through fixed points: the fixed point h lists h, then (r, v_r) for r = 0..3, where fixed point 0 has v = 0, and the fixed points from 1 on take, in turn, for each vector u below, each s in {0, 2} and each m in {1, 121, 11}, v = m w, where w_(r + s mod 4) = u_r - u_(-s mod 4). Pure representatives: {(0,0), (0,60), (0,129), (0,49), (1,17)} {(0,0), (0,24), (0,130), (0,115), (3,72)} {(0,0), (0,40), (0,119), (0,6), (2,5)} {(0,0), (0,10), (1,28), (2,42), (3,71)} {(0,0), (0,8), (1,77), (2,31), (3,30)} {(0,0), (0,16), (1,120), (2,64), (3,58)} {(1,0), (1,14), (1,4), (1,87), (2,33)} {(0,0), (1,70), (1,112), (1,129), (1,78)} {(1,0), (1,36), (1,111), (1,30), (3,88)} {(0,0), (1,68), (1,56), (2,104), (3,124)} {(0,0), (1,81), (1,34), (2,115), (3,1)} {(0,0), (1,16), (1,9), (2,99), (3,7)} Vectors: (0,10,117,21); (0,5,20,24); (0,27,72,53); (0,46,88,110); (0,71,56,23); (0,58,3,128); (0,15,54,93); (0,1,2,68); (0,3,40,38) Equation 255: satisfied. Idempotent elements: 131.

last edited by qawbecrdtey at 2026-10-08 15:15:46 · history