/*
www-ATLAS of Group Representations.
TD4(2) represented as permutations on 819 points.
*/

G<x,y>:=PermutationGroup<819|\[
2,1,5,7,3,10,4,13,15,6,18,20,8,23,9,26,28,11,31,12,34,35,14,38,33,
16,42,17,45,47,19,50,25,21,22,55,57,24,60,62,64,27,67,54,29,71,30,74,49,32,
78,80,82,44,36,86,37,89,91,39,94,40,96,41,99,98,43,103,104,106,46,109,111,48,114,
116,118,51,121,52,124,53,127,129,131,56,87,135,58,138,59,141,143,61,146,63,148,66,65,152,
154,156,68,69,159,70,162,164,72,165,73,167,169,75,171,76,174,77,177,179,79,182,183,81,186,
188,83,190,84,193,85,196,198,200,88,203,205,90,207,209,92,212,93,215,217,95,220,97,222,224,
226,100,229,101,232,102,235,236,105,239,241,107,244,108,110,247,112,250,113,253,115,255,257,117,260,
262,119,265,120,180,269,122,123,273,275,125,277,126,189,128,281,283,130,194,242,132,288,133,290,134,
293,295,136,297,137,300,139,303,140,305,307,142,310,311,144,274,145,316,318,147,321,149,285,150,325,
151,328,330,153,280,334,155,336,338,157,158,339,341,160,344,161,195,346,163,349,351,166,354,356,168,
359,361,170,364,172,367,173,263,371,175,373,176,258,376,178,317,379,375,181,383,385,387,184,216,185,
391,187,358,393,230,191,397,192,399,223,401,403,197,406,199,408,410,201,413,202,416,204,419,421,206,
340,302,208,426,210,429,211,312,432,213,214,308,436,437,439,218,266,219,444,446,221,448,323,450,225,
402,452,227,455,228,457,332,333,231,462,233,463,234,237,301,238,465,467,240,380,243,352,471,245,474,
246,347,476,248,478,249,480,278,251,422,252,386,484,254,425,423,256,487,488,370,259,491,261,492,268,
264,495,496,267,345,497,499,270,502,271,362,272,506,508,510,276,513,279,516,459,396,282,518,284,521,
286,326,287,524,525,289,515,291,529,292,532,534,294,536,537,296,540,539,298,544,299,360,366,546,365,
304,549,551,306,553,550,309,557,559,561,313,314,565,315,568,569,571,573,319,576,320,578,322,579,324,
581,327,584,586,329,589,331,591,395,594,545,335,337,596,342,466,343,585,483,601,348,602,604,350,606,
353,608,355,609,357,612,614,469,363,485,616,368,369,595,619,372,374,621,519,377,378,381,625,382,620,
628,384,503,629,631,388,632,389,634,390,600,638,392,641,407,394,535,398,494,592,400,647,640,404,405,
651,563,654,409,657,603,411,643,412,517,414,415,661,418,417,659,653,543,420,461,424,574,635,427,431,
428,618,430,665,673,660,433,676,434,679,435,682,527,633,438,658,613,440,441,688,442,666,443,547,693,
445,694,447,449,697,451,698,639,453,468,454,683,588,456,704,458,520,663,460,489,464,691,702,709,511,
470,472,531,473,715,475,717,477,479,687,720,481,567,482,723,486,669,552,490,500,493,727,623,728,498,
675,730,501,504,732,505,507,564,509,548,648,736,512,583,523,514,664,533,655,722,672,522,636,745,746,
526,716,542,528,644,749,530,566,541,556,538,701,593,642,554,572,708,754,617,707,695,646,555,719,626,
558,755,737,560,726,681,562,587,706,765,767,610,570,770,690,597,773,575,577,671,775,580,582,712,739,
662,598,778,590,763,684,670,667,599,782,783,699,784,785,605,652,607,786,674,611,789,645,615,791,757,
680,622,624,793,627,794,630,760,795,787,637,678,798,700,799,801,753,744,743,649,650,796,756,656,772,
804,805,742,668,677,748,725,780,777,733,766,807,705,790,685,761,686,808,809,689,810,750,692,797,696,
800,759,703,788,758,812,710,711,713,714,718,735,779,721,764,724,816,729,731,734,747,774,738,740,776,
741,817,811,751,752,815,762,768,769,771,803,781,818,819,806,792,802,813,814]
,\[
3,4,6,8,9,11,12,14,16,17,19,21,22,24,25,27,29,30,32,33,7,36,37,39,40,
41,43,44,46,48,49,51,52,53,54,56,58,59,61,63,65,66,68,69,70,72,73,75,76,77,
79,81,83,84,85,87,88,90,92,93,95,31,97,98,100,101,102,67,105,107,108,110,112,113,115,
117,119,120,122,123,125,126,128,130,132,133,134,136,137,139,140,142,144,145,147,121,149,150,151,153,
155,157,99,158,160,161,163,28,15,166,131,168,138,170,172,173,175,176,178,180,181,1,184,185,187,
189,177,191,192,194,195,197,199,201,202,204,20,206,208,210,211,213,214,216,218,219,2,221,223,225,
227,228,230,231,233,234,5,237,238,240,242,243,245,246,135,248,249,251,252,164,254,256,258,259,261,
263,264,266,267,268,270,271,272,274,276,143,278,279,280,193,282,174,284,285,286,287,224,289,291,292,
294,229,296,298,299,301,302,179,304,306,308,309,167,312,313,314,315,317,319,320,322,323,324,156,326,
327,329,331,332,333,335,207,337,300,82,118,340,342,343,260,345,42,347,348,350,352,353,355,357,358,
360,362,363,365,366,368,369,370,372,71,361,374,375,377,378,159,380,381,382,384,386,310,388,389,390,
104,392,89,394,395,396,257,398,400,182,402,404,405,239,407,409,411,412,414,415,417,418,420,422,423,
424,425,148,427,428,269,430,431,433,86,434,435,341,438,440,441,442,443,445,351,447,449,198,109,235,
451,453,454,200,456,458,459,460,461,339,305,106,336,367,464,290,466,265,468,469,273,470,472,473,475,
387,471,477,38,10,479,354,247,462,481,482,483,80,485,262,45,486,446,489,379,490,436,205,493,346,
494,406,492,196,23,498,500,501,503,504,35,505,507,509,511,512,514,515,283,517,397,518,519,520,522,
338,523,215,502,526,527,496,528,530,531,533,535,448,13,538,539,541,542,543,437,545,457,55,547,190,
548,550,552,450,554,555,556,558,560,562,563,564,566,567,444,570,572,574,575,577,18,288,91,580,484,
582,583,585,587,588,590,455,592,593,595,408,78,373,597,598,50,599,600,601,429,452,603,605,169,255,
607,209,165,610,611,613,62,349,615,303,617,385,618,34,620,506,222,622,623,465,488,624,626,627,413,
293,116,399,630,416,410,236,633,635,636,637,639,640,642,569,281,643,644,594,645,646,232,648,649,650,
652,653,655,656,183,658,557,103,659,660,421,508,540,662,663,664,665,666,661,516,667,608,668,669,250,
670,671,672,94,674,480,675,677,678,680,681,467,683,684,685,686,383,687,657,689,690,307,691,692,679,
241,621,695,696,651,474,604,699,371,700,701,203,702,703,596,705,499,706,707,26,708,124,426,710,146,
711,712,713,714,581,716,718,719,573,576,546,721,722,723,724,561,497,403,725,726,344,586,682,154,729,
359,731,632,188,733,734,571,491,735,253,334,737,738,532,739,740,741,325,536,96,742,743,744,612,747,
364,748,647,495,578,432,750,751,752,753,419,754,619,755,277,756,757,758,244,614,759,609,141,760,513,
761,602,762,534,763,544,727,764,57,766,768,769,728,771,393,772,311,774,321,510,226,776,698,114,777,
171,463,553,779,780,478,629,730,781,186,356,606,775,64,641,212,152,787,74,788,790,47,487,162,792,
521,591,525,676,782,717,111,551,565,796,797,778,794,391,800,297,802,127,732,589,803,704,791,631,628,
537,217,439,220,328,616,529,806,785,783,799,275,318,129,801,805,715,60,476,767,784,745,524,688,786,
316,808,559,693,811,625,813,673,814,401,549,815,809,295,638,694,789,793,773,634,807,749,812,746,817,
795,584,709,330,736,654,818,579,720,765,376,770,804,697,816,568,798,810,819]
>;
print "Group G is TD4(2) < Sym(819)";