Equation 677 Database

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Magma 6fe9c8cb636f…

magma 6fe9c8cb636f
Size
557
Isomorphism class hash
6fe9c8cb636f6e17ec96dd735ebc9380556e617f0538ff9e9e0e145a2aeebab7
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 556) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 15:26:09
Display reorder
556,36,26,7,37,14,18,42,27,32,4,40,8,6,43,39,38,3,22,0,15,47,30,23,19,25,17,1,44,21,29,16,28,11,12,45,33,35,13,31,5,2,46,24,41,10,34,20,9,552,217,117,418,127,334,169,172,327,179,406,289,255,100,299,188,252,167,288,235,316,450,263,253,96,446,215,106,158,224,164,471,444,143,63,493,284,310,125,517,191,367,67,540,361,119,448,346,307,424,240,246,182,445,227,73,180,60,145,268,155,209,308,377,199,469,365,94,396,495,286,443,351,516,431,196,274,543,156,109,385,130,340,468,398,126,335,494,376,197,473,518,202,337,492,542,251,241,520,260,91,278,544,233,470,447,128,338,496,412,320,472,519,291,336,497,541,287,242,521,139,306,83,545,285,239,64,554,218,115,421,111,70,170,356,330,438,409,436,256,99,297,186,49,165,208,236,317,451,264,249,97,303,213,105,159,222,162,459,113,142,61,480,78,311,81,505,193,368,68,528,359,120,441,344,435,422,89,247,183,153,230,74,177,58,175,266,355,210,437,378,200,458,363,93,394,483,140,135,357,504,439,55,272,531,122,108,386,131,341,456,399,87,150,481,374,194,461,506,201,244,482,529,53,102,508,258,90,281,532,232,457,413,123,332,484,410,319,460,507,292,77,485,530,204,237,509,137,66,354,533,434,52,76,553,383,206,420,112,141,171,174,329,56,408,282,294,382,298,187,389,166,390,453,402,455,401,248,211,302,257,219,161,223,387,465,318,452,400,486,79,314,80,511,192,372,69,534,358,342,440,345,271,423,184,293,185,369,229,205,176,85,149,265,270,212,304,384,221,464,362,370,393,488,148,134,353,510,433,381,273,536,220,160,392,132,343,463,405,88,151,491,373,380,467,515,388,245,487,539,404,103,513,259,312,280,537,231,462,414,391,331,489,454,403,466,512,296,313,490,535,207,371,514,136,147,86,538,98,295,379,555,216,116,419,322,71,168,173,328,57,407,283,254,101,300,190,48,275,261,234,315,449,349,250,426,301,214,107,157,226,163,476,114,144,62,498,189,309,82,522,347,366,425,546,360,118,442,350,269,430,225,325,181,154,228,72,178,59,146,267,104,348,305,429,198,478,364,95,395,501,427,133,352,523,432,54,277,549,121,110,416,129,339,474,397,321,152,500,375,195,479,524,203,243,499,547,50,276,526,262,92,279,550,323,475,417,124,333,502,411,326,477,525,290,75,503,548,428,238,527,138,65,84,551,324,51,415 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 557 = 49 + 4*127, glued along a group-divisible design developed from base blocks under the translations of Z/127; blocks of five points. Points: 0..48 are fixed points; 49 + 127r + a is the point (r, a), r in 0..3, a in Z/127. The fixed points form one group, the hole, and carry A(49;18,8,0): x*y = 18x + 8y mod 49; every other point is a group of its own and squares to itself. 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/127, of the base blocks. Pure base blocks: for each representative B below, each s in {0, 2} and each m in {1, 19, 107}, 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, 19, 107}, v = m w, where w_(r + s mod 4) = u_r - u_(-s mod 4). Pure representatives: {(0,0), (0,39), (0,14), (0,89), (1,67)} {(0,0), (0,59), (0,124), (0,114), (3,49)} {(0,0), (0,36), (0,116), (0,107), (2,124)} {(0,0), (0,46), (1,1), (2,82), (3,23)} {(0,0), (0,32), (1,63), (2,6), (3,44)} {(0,0), (0,58), (1,106), (2,123), (3,121)} {(1,0), (1,32), (1,111), (1,121), (2,120)} {(0,0), (1,45), (1,94), (1,41), (1,42)} {(1,0), (1,30), (1,55), (1,69), (3,66)} {(0,0), (1,20), (1,9), (2,5), (3,26)} {(0,0), (1,72), (1,26), (2,55), (3,8)} {(0,0), (1,33), (1,101), (2,90), (3,21)} Vectors: (0,78,83,126); (0,13,48,43); (0,71,10,80); (0,5,108,33); (0,4,15,2); (0,66,61,91); (0,64,125,59); (0,65,103,22) Equation 255: satisfied. Idempotent elements: 509.

last edited by qawbecrdtey at 2026-10-08 15:26:12 · history