/*
www-ATLAS of Group Representations.
6.L3(4) represented as permutations on 720 points.
*/

G<x,y>:=PermutationGroup<720|\[
2,1,11,8,16,10,18,4,23,6,3,29,26,28,32,5,35,7,38,36,37,41,9,44,45,
13,49,14,12,52,54,15,57,60,17,20,21,19,63,65,22,68,71,24,25,73,74,75,27,76,
77,30,81,31,83,85,33,69,88,34,92,93,39,97,40,99,101,42,58,104,43,108,46,47,48,
50,51,110,112,113,53,116,55,100,56,121,124,59,105,126,129,61,62,132,134,135,64,138,66,84,
67,143,146,70,89,148,151,72,153,78,158,79,80,130,163,82,165,167,168,162,86,173,172,87,177,
90,181,180,91,114,184,94,189,95,96,152,194,98,196,198,199,193,102,204,203,103,208,106,212,211,
107,136,109,219,216,218,222,111,215,224,225,120,115,229,117,232,118,119,237,238,241,123,122,245,246,
249,125,251,254,128,127,258,259,131,264,261,263,267,133,260,269,270,142,137,274,139,277,140,141,282,
283,286,145,144,290,291,294,147,296,299,150,149,303,304,159,155,307,156,154,310,312,157,314,160,161,
319,272,230,164,228,323,166,326,328,329,331,169,170,335,316,171,339,340,343,174,175,348,347,176,352,
178,356,355,179,360,361,364,182,183,190,186,370,187,185,373,375,188,377,191,192,382,227,275,195,273,
386,197,389,391,351,393,200,201,397,379,202,399,400,403,205,206,408,407,207,353,209,413,412,210,415,
416,419,213,214,423,424,217,427,428,220,433,221,435,223,378,240,439,442,226,444,384,445,231,448,450,
233,453,234,235,456,236,459,461,462,239,465,466,468,242,243,362,472,244,476,477,406,248,247,483,410,
280,250,295,486,253,252,490,491,493,255,256,341,497,257,501,502,504,505,496,262,507,508,265,455,266,
482,268,315,285,515,518,271,520,321,521,276,522,524,278,527,279,529,281,530,532,533,284,536,287,288,
417,539,289,543,544,346,293,292,436,350,434,298,297,552,300,301,401,425,302,557,558,560,305,306,418,
564,308,309,440,555,567,549,311,411,313,409,572,573,317,429,576,318,580,320,322,585,586,324,460,325,
589,526,327,528,374,330,535,464,332,449,333,334,597,458,336,337,602,338,605,606,538,342,498,583,542,
344,345,613,612,547,615,376,349,485,484,354,512,619,603,357,358,620,359,584,591,369,363,473,510,624,
365,366,568,367,368,628,371,372,516,499,595,487,621,632,380,509,634,381,638,383,385,387,531,388,644,
452,390,454,392,394,523,395,396,650,457,398,653,471,402,554,641,475,404,405,625,574,480,563,432,660,
600,414,645,540,430,590,420,421,631,422,663,664,548,426,667,668,431,503,577,651,648,437,438,546,671,
441,569,636,673,443,674,675,474,494,446,447,599,643,451,556,495,683,679,617,511,659,463,616,587,551,
604,467,489,601,469,470,690,655,691,657,692,479,478,649,481,598,594,635,488,492,513,696,697,500,545,
695,676,506,700,701,559,514,702,517,618,578,688,519,686,704,541,652,588,525,553,706,677,571,614,534,
570,642,537,707,608,682,610,685,596,550,708,694,561,562,669,711,565,566,665,681,575,714,579,581,582,
627,647,680,593,678,670,656,592,698,658,639,689,637,687,607,609,611,705,662,626,622,623,684,717,629,
630,633,715,640,693,646,654,661,710,709,666,713,712,672,703,718,699,716,720,719]
,\[
3,7,12,13,1,14,19,20,2,21,25,5,30,31,4,33,6,27,9,39,40,8,42,10,18,
46,11,47,51,15,17,55,58,16,59,48,50,62,22,24,66,69,23,70,64,36,37,26,53,28,
49,78,29,79,84,32,86,34,89,90,35,45,94,38,95,100,41,102,43,105,106,44,96,98,80,
82,109,75,76,52,114,54,117,56,119,122,57,123,61,127,60,128,131,73,74,63,136,65,139,67,
141,144,68,145,72,149,71,150,154,155,77,156,129,161,81,162,166,83,169,85,170,87,174,175,88,
178,91,182,183,92,185,186,93,187,151,192,97,193,197,99,200,101,201,103,205,206,104,209,107,213,
214,108,215,111,220,221,110,223,112,113,115,226,227,116,230,118,233,235,120,239,121,240,243,125,247,
124,248,252,126,253,256,130,160,260,133,265,266,132,268,134,135,137,271,272,138,275,140,278,280,142,
284,143,285,288,147,292,146,293,297,148,298,301,152,191,305,158,153,222,309,157,159,313,306,315,317,
164,320,163,321,322,165,324,327,167,330,168,332,229,171,336,337,172,341,173,342,345,176,349,350,177,
353,179,357,358,180,362,181,363,366,368,189,184,267,372,188,190,376,369,378,380,195,383,194,384,385,
196,387,390,198,392,199,394,274,202,398,338,203,401,204,402,405,207,409,410,208,352,210,414,359,211,
417,212,418,421,217,216,425,218,429,430,219,431,308,436,438,224,440,225,441,228,334,231,446,449,232,
451,234,454,294,236,457,460,237,238,463,242,286,241,467,470,244,473,474,245,478,246,479,481,250,433,
249,484,485,251,391,488,255,299,254,492,495,257,498,499,258,503,259,262,261,497,263,509,510,264,511,
371,483,514,269,516,270,517,273,396,276,447,523,277,525,279,528,281,458,531,282,283,534,287,469,537,
289,540,541,290,545,291,546,548,295,455,296,328,550,300,494,553,302,554,555,303,559,304,527,416,563,
307,530,566,311,568,569,310,351,312,408,571,314,316,574,318,577,578,319,581,583,386,323,579,325,587,
590,326,591,549,329,592,393,331,594,333,595,593,598,335,599,600,399,603,339,580,340,607,344,609,343,
597,611,346,614,347,616,348,617,411,354,375,355,573,356,582,536,415,465,360,622,361,615,365,623,364,
508,544,367,608,453,370,459,630,374,631,618,373,377,379,612,381,635,636,382,639,641,637,388,642,624,
389,645,487,646,648,395,567,647,651,397,652,638,400,654,404,656,403,650,658,406,659,407,570,412,632,
413,640,562,420,661,419,428,477,422,655,423,424,426,665,427,613,669,432,434,435,437,491,489,670,439,
644,443,448,442,471,490,444,676,445,677,679,681,450,682,452,627,462,456,629,684,461,685,464,621,673,
466,686,688,468,674,687,504,472,475,476,662,693,557,480,506,482,513,486,694,521,493,496,500,526,501,
502,505,698,507,625,512,551,515,589,519,522,518,538,552,520,663,705,524,691,561,533,529,565,532,692,
535,572,689,560,539,542,543,626,547,695,556,558,620,668,710,564,708,713,649,575,675,576,601,653,702,
584,690,585,707,586,588,703,715,596,610,606,602,604,605,678,672,657,633,660,619,701,717,718,628,697,
720,704,634,671,643,714,680,711,664,666,712,667,709,683,706,696,719,699,700,716]
>;
print "Group G is 6.L3(4) < Sym(720)";