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

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