/*
www-ATLAS of Group Representations.
J2 represented as permutations on 840 points.
*/

G<x,y>:=PermutationGroup<840|\[
2,1,5,7,3,10,4,12,13,6,16,8,9,20,21,11,24,25,27,14,15,31,32,17,18,
36,19,38,39,41,22,23,45,46,48,26,51,28,29,55,30,57,58,59,33,34,63,35,65,66,
37,67,68,70,40,73,42,43,44,77,78,80,47,83,49,50,52,53,89,54,91,72,56,92,93,
95,60,61,99,62,101,102,64,103,104,106,108,110,69,113,71,74,75,118,76,120,121,123,79,126,
81,82,84,85,132,86,134,87,136,88,138,139,90,140,141,142,144,94,147,96,97,151,98,153,154,
100,155,156,158,160,162,105,165,107,168,109,171,111,112,114,115,116,177,117,179,180,119,181,182,184,
122,187,124,125,127,128,193,129,195,130,197,131,199,200,133,201,202,135,205,206,137,207,208,210,212,
214,143,217,145,146,148,149,223,150,224,186,152,225,226,228,230,192,157,234,159,237,161,240,163,164,
166,167,204,203,169,170,172,173,251,174,253,175,255,176,257,258,178,259,260,262,264,266,183,185,188,
189,272,190,274,191,276,277,278,194,279,280,196,283,284,198,285,286,288,290,292,294,295,297,250,249,
209,302,211,305,213,308,215,216,218,219,314,220,316,221,318,222,320,321,322,323,325,227,328,229,331,
231,232,233,235,236,282,281,238,239,241,242,342,243,344,244,345,245,347,246,247,350,248,298,352,353,
354,252,355,356,254,359,360,256,361,362,364,366,368,261,371,263,374,265,377,267,268,269,270,382,271,
384,385,273,386,387,275,390,391,392,335,395,397,398,400,402,379,287,406,289,291,409,293,412,414,296,
407,299,300,301,303,304,358,357,306,307,309,310,422,311,423,312,425,313,427,428,315,429,430,317,433,
434,319,435,341,437,439,324,442,326,327,329,330,389,388,332,333,334,450,451,336,417,337,338,454,339,
456,340,458,459,460,343,351,461,346,410,462,348,465,349,467,469,396,471,473,420,476,363,365,480,367,
483,369,370,372,373,432,431,375,376,378,493,380,495,381,497,498,383,444,443,501,503,504,506,507,393,
394,511,470,399,487,401,516,403,404,405,408,411,523,524,413,527,415,530,416,453,418,533,419,535,536,
421,538,539,540,424,543,544,426,545,546,548,455,488,513,550,532,509,436,518,438,556,440,441,560,500,
445,561,446,447,564,448,449,566,492,567,452,552,489,568,569,457,572,494,573,575,577,578,463,464,581,
582,466,583,576,468,586,491,472,590,474,475,594,477,478,479,542,541,481,482,484,485,604,486,606,490,
608,512,609,610,611,496,612,613,615,499,502,617,619,505,622,508,510,514,515,571,570,517,519,629,520,
529,521,522,632,633,525,526,528,637,638,531,607,639,640,534,641,642,643,537,644,645,647,649,651,602,
653,600,656,547,659,549,587,551,553,554,555,557,558,668,559,669,562,672,563,636,674,565,675,676,678,
661,681,682,574,685,687,579,580,691,693,620,584,585,588,589,591,592,593,595,596,699,597,701,598,684,
599,704,601,706,707,603,709,710,605,711,626,662,703,712,714,697,717,614,616,721,722,618,725,621,623,
624,728,625,679,729,627,628,732,650,630,686,631,733,724,735,634,737,635,739,740,742,666,745,646,720,
648,749,663,652,751,654,655,727,657,658,660,664,713,665,756,757,667,759,760,700,670,671,762,689,673,
763,708,677,680,765,767,683,688,770,690,772,692,774,694,695,776,696,778,779,698,781,782,775,702,783,
705,752,784,755,754,715,716,786,718,719,789,723,726,773,730,793,731,795,796,734,798,736,764,738,748,
741,801,743,744,803,746,747,750,753,806,758,808,809,761,805,812,813,766,816,768,769,819,771,820,821,
777,807,780,814,790,785,802,787,788,822,825,791,792,804,827,794,828,829,797,799,800,810,830,833,811,
834,815,817,818,823,832,831,824,826,835,839,837,840,836,838]
,\[
3,4,6,8,9,1,11,2,14,15,17,18,19,5,22,23,7,26,28,29,30,10,33,34,35,
12,37,13,40,42,43,44,16,47,49,50,52,53,54,20,56,21,59,60,61,62,24,64,25,51,
36,27,69,71,72,74,75,76,31,32,79,81,82,84,85,86,87,88,38,90,39,73,55,41,94,
96,97,98,45,100,46,83,63,48,105,107,109,111,112,114,115,116,117,57,119,58,122,124,125,127,
128,129,130,131,65,133,66,135,67,137,68,113,89,70,142,143,145,146,148,149,150,77,152,78,126,
99,80,157,159,161,163,164,166,167,169,170,172,173,174,175,176,91,92,178,93,147,118,95,183,185,
186,188,189,190,191,192,101,194,102,196,103,198,104,165,132,106,203,204,108,171,136,110,209,211,213,
215,216,218,219,220,221,222,120,223,121,187,151,123,227,229,231,232,233,235,236,238,239,241,242,243,
244,245,134,246,247,248,249,250,138,252,139,254,140,256,141,217,177,144,261,263,265,267,268,269,270,
271,153,273,154,275,155,156,234,193,158,281,282,160,240,197,162,287,289,291,293,168,296,298,299,300,
301,303,304,306,307,309,310,311,312,313,179,315,180,317,181,319,182,184,323,324,326,327,329,330,332,
333,276,334,335,336,195,337,338,339,340,341,199,343,200,295,201,346,202,348,349,205,351,206,207,208,
302,251,210,357,358,212,308,255,214,363,365,367,369,370,372,373,375,376,378,379,380,381,224,225,383,
226,328,272,228,388,389,230,277,393,394,396,237,399,401,403,404,405,354,407,408,410,411,413,290,344,
353,352,297,288,415,416,253,417,418,419,420,421,257,422,258,424,259,426,260,371,314,262,431,432,264,
377,318,266,436,438,440,441,386,443,444,325,445,274,446,447,448,449,278,279,452,280,453,430,283,455,
284,457,285,286,406,342,350,409,345,292,463,464,294,466,468,470,305,472,474,475,477,478,479,481,482,
484,485,486,487,488,316,489,490,491,492,320,494,321,496,322,442,382,499,500,502,331,505,507,508,509,
510,512,513,429,514,515,517,518,519,520,521,522,347,525,526,528,529,355,531,356,532,359,534,360,361,
537,362,364,541,542,366,483,425,368,547,549,454,398,374,551,552,553,458,554,555,557,558,559,384,385,
498,387,562,563,390,565,391,392,567,511,451,395,397,400,570,571,402,493,574,576,578,579,580,523,412,
527,465,414,584,585,587,588,589,591,592,593,595,596,597,598,423,599,600,601,602,603,427,605,428,607,
433,434,435,437,556,495,439,614,501,560,616,618,620,621,623,624,450,625,626,456,627,628,609,459,630,
460,631,461,462,524,634,635,636,467,586,530,469,471,590,533,473,643,594,536,476,646,648,650,480,652,
654,655,657,658,660,661,640,662,663,664,665,666,667,497,668,670,671,503,673,504,622,564,506,677,679,
680,516,683,684,686,688,689,690,692,674,687,649,694,608,550,695,696,535,697,698,538,700,539,702,540,
703,543,705,544,545,708,546,659,604,548,678,639,573,713,715,716,718,719,720,561,723,724,726,582,710,
727,566,606,568,569,730,731,572,685,629,575,583,577,734,736,735,581,738,740,741,743,744,746,669,747,
748,637,728,750,752,753,676,754,709,755,693,732,610,712,611,612,758,613,615,699,761,721,617,725,672,
619,707,651,764,766,768,714,769,632,771,633,773,711,775,638,641,777,642,644,780,645,647,749,701,751,
704,653,783,656,675,785,778,787,742,788,722,790,733,791,792,681,794,682,763,797,691,772,774,737,799,
800,759,786,802,804,805,760,706,784,807,757,717,782,810,811,729,814,815,817,818,796,798,770,739,801,
776,803,779,745,822,823,756,808,821,824,762,826,812,765,816,793,767,830,825,831,832,781,827,789,834,
813,806,835,836,795,837,809,833,819,838,840,820,828,839,829]
>;
print "Group G is J2 < Sym(840)";