/*
www-ATLAS of Group Representations.
5^(2+2+4):(S3 x GL2(5)) represented as permutations on 750 points.
*/

G<x,y>:=PermutationGroup<750|\[
2,4,6,8,10,11,13,1,16,18,20,22,7,25,27,29,31,33,35,3,38,40,42,44,46,
48,50,52,54,56,58,60,5,62,64,66,68,51,71,73,75,77,79,81,83,85,87,45,90,91,
93,95,96,9,99,101,103,104,106,108,110,112,114,116,118,120,34,123,125,127,129,131,12,134,136,
138,140,142,144,146,148,150,26,152,14,154,155,157,159,161,15,137,21,165,167,168,170,172,174,176,
178,180,182,17,185,187,189,190,192,194,196,67,199,201,203,19,198,207,209,210,55,179,214,216,218,
220,173,164,223,225,149,227,143,230,231,233,235,236,238,23,241,243,245,247,249,250,251,24,254,256,
258,260,261,263,265,57,244,266,268,270,205,273,274,276,278,280,28,282,283,285,287,289,291,121,294,
296,221,30,300,302,304,156,255,308,309,311,313,195,316,32,319,320,322,324,326,328,330,332,334,336,
337,175,338,340,49,343,345,347,119,36,351,352,354,37,356,348,358,360,323,286,193,364,39,349,367,
369,371,293,374,376,378,379,41,310,381,383,385,387,327,389,391,392,394,395,397,399,43,217,402,403,
405,407,408,72,411,413,415,417,396,420,318,204,422,423,47,426,428,430,432,434,97,111,298,439,441,
442,444,446,447,448,449,53,440,418,271,370,453,454,456,158,70,457,460,461,350,464,466,468,470,471,
472,473,331,474,475,476,478,295,481,482,421,414,59,486,346,488,458,490,427,493,494,177,219,61,497,
498,500,272,502,504,506,507,451,510,512,357,63,513,452,515,516,517,206,520,65,521,499,524,525,184,
528,511,530,284,532,533,534,508,462,69,183,538,540,325,380,315,487,436,544,126,545,186,548,306,550,
74,483,553,299,555,92,558,76,561,237,541,443,465,240,301,401,567,569,78,88,297,133,571,573,373,
141,557,80,577,579,495,581,582,583,166,361,535,82,588,589,586,591,213,275,84,372,86,595,455,596,
290,480,267,599,89,602,603,368,522,503,604,228,365,607,608,609,128,139,611,613,94,342,410,560,597,
518,339,477,359,618,98,600,620,463,437,202,288,623,100,625,259,627,162,628,232,122,631,102,549,606,
229,171,450,636,191,105,562,640,641,642,416,130,107,644,153,388,568,109,575,650,384,222,188,653,547,
622,655,656,658,585,543,117,248,621,113,542,341,115,242,262,335,279,663,664,638,366,160,578,124,667,
668,292,670,580,485,672,509,615,200,675,587,645,677,679,678,680,212,303,682,132,634,239,657,181,632,
344,686,135,539,438,669,145,479,563,614,659,234,693,305,565,652,514,692,556,624,431,662,696,253,666,
697,698,523,147,699,584,574,616,252,536,314,505,683,660,630,151,619,706,594,612,709,307,710,695,527,
643,398,674,433,713,564,163,169,419,610,716,264,572,281,215,718,425,665,593,702,355,722,723,552,491,
694,519,725,689,714,390,711,720,526,726,382,605,551,707,687,673,353,601,633,651,688,647,728,529,729,
705,731,208,654,732,733,400,197,496,257,404,445,333,467,424,321,224,546,393,211,690,712,734,269,715,
736,738,740,719,685,646,226,312,637,386,570,377,742,703,724,691,743,744,708,739,246,721,661,649,566,
626,317,741,590,537,592,747,701,617,717,375,748,684,704,412,277,735,409,554,489,730,746,459,727,750,
635,671,648,406,576,700,329,435,484,598,749,639,362,429,363,629,681,492,559,676,501,737,531,745,469]
,\[
3,5,7,9,2,12,14,15,17,19,21,23,24,26,28,30,32,34,36,37,39,41,43,45,47,
49,51,53,55,57,59,1,61,63,65,67,69,70,72,74,76,78,80,82,84,86,88,89,4,92,
94,42,97,98,100,102,99,105,107,109,111,113,115,117,119,121,122,124,126,128,130,132,133,135,137,
139,141,143,145,147,149,116,151,153,64,81,156,158,160,90,162,163,164,166,35,169,171,173,175,177,
179,181,183,184,186,188,123,191,193,195,197,198,200,202,204,205,206,208,31,211,212,213,215,217,219,
221,222,10,224,226,77,228,229,52,232,234,134,237,239,240,242,244,246,248,11,6,252,253,255,257,
259,152,262,264,104,25,140,267,269,271,272,260,275,277,279,281,176,178,284,286,288,290,292,293,295,
297,298,299,301,303,305,306,307,243,310,312,314,315,317,318,125,321,323,325,327,329,331,333,335,54,
280,332,339,341,342,344,346,348,349,350,75,353,355,334,357,96,359,22,361,362,363,365,366,91,368,
370,372,373,375,377,296,106,62,380,382,384,386,388,343,390,167,393,385,396,398,120,400,401,118,404,
406,330,409,410,412,414,416,418,419,129,50,421,371,424,425,427,429,431,433,435,436,437,438,440,294,
443,445,320,338,347,27,20,450,142,451,452,254,455,457,423,458,459,383,462,463,465,467,469,180,250,
199,235,358,309,447,477,479,480,190,381,483,484,485,395,487,489,356,491,492,304,192,73,495,496,474,
499,411,501,503,505,33,508,509,511,101,506,498,514,155,138,182,518,519,85,316,522,523,497,526,527,
529,218,326,531,38,256,95,535,536,444,537,539,541,364,542,543,413,482,168,300,546,547,549,402,551,
552,442,554,322,556,557,559,560,562,563,564,354,565,566,432,493,568,131,68,337,545,570,572,574,476,
575,360,576,578,500,580,251,165,584,585,558,586,587,241,236,590,308,592,593,291,594,245,548,544,597,
426,598,555,600,601,261,515,473,521,481,48,605,606,472,577,274,610,478,612,273,446,392,263,614,185,
615,302,616,617,619,448,93,613,582,621,154,622,624,434,456,626,189,428,629,630,415,632,633,631,161,
634,602,635,420,637,638,639,573,58,405,643,550,561,645,646,647,319,648,649,651,652,608,187,596,520,
654,210,657,207,146,659,595,324,510,660,603,387,513,470,468,661,662,276,665,313,285,664,666,591,247,
29,669,249,671,148,287,673,674,258,628,417,676,678,454,488,607,150,681,214,683,460,170,684,79,685,
581,56,525,687,688,689,690,110,227,553,691,692,694,196,66,695,289,636,422,516,528,569,464,270,112,
103,399,679,216,700,701,233,702,530,682,703,704,60,650,699,705,698,83,707,708,238,618,588,599,711,
706,18,712,345,475,567,625,714,203,715,517,675,403,717,697,719,720,721,640,620,231,268,718,583,282,
724,672,709,209,589,726,336,534,174,44,376,394,441,713,8,571,538,278,727,604,490,486,696,397,730,
266,453,466,439,46,734,667,677,732,144,735,494,663,693,352,201,340,728,502,540,656,623,108,351,733,
737,739,533,741,13,731,740,579,172,40,194,742,157,136,658,225,389,653,609,710,220,311,159,745,407,
746,16,729,722,644,744,680,748,369,471,87,461,670,641,230,749,374,750,114,391,367,265,747,504,668,
378,524,716,655,408,223,328,449,642,611,736,532,430,283,512,71,686,507,738,127,379,723,743,725,627]
>;
print "Group G is 5^(2+2+4):(S3 x GL2(5)) < Sym(750)";