/* www-ATLAS of Group Representations. 32.U4(3):D8 represented as permutations on 756 points. */ G:=PermutationGroup<756|\[ 1,4,6,2,10,3,14,15,9,5,20,12,22,7,8,27,29,30,19,11,34,13,37,38,39, 26,16,28,17,18,31,32,33,21,35,51,23,24,25,58,59,42,43,44,64,46,67,69,49,50, 36,52,75,54,78,56,57,40,41,86,88,89,91,45,94,96,47,68,48,101,103,72,73,106,53, 110,111,55,114,115,117,118,120,122,124,60,128,61,62,133,63,136,138,65,95,66,143,145,147,149, 70,153,71,155,157,74,160,161,163,76,77,112,169,79,80,174,81,82,119,83,121,84,182,85,179, 186,127,87,141,130,193,132,90,197,135,92,202,93,203,205,129,172,97,211,98,214,99,191,100,219, 151,221,102,224,104,226,105,158,168,107,108,176,109,236,165,238,228,159,113,243,245,142,173,116,175, 162,177,178,125,256,181,123,260,184,185,126,229,265,266,190,148,239,131,271,272,274,134,275,277,278, 279,137,139,284,140,287,207,289,290,292,144,295,213,146,215,299,300,302,150,305,152,307,308,154,225, 156,227,167,187,230,315,232,317,234,319,164,322,166,192,325,241,327,170,330,171,332,333,335,336,338, 340,285,342,343,329,180,347,349,350,183,352,353,263,355,188,189,360,268,361,363,194,195,367,196,198, 304,199,200,201,376,377,379,381,204,252,386,206,390,208,209,395,210,293,306,212,402,297,403,216,217, 301,218,411,276,220,294,222,223,419,420,421,423,425,427,231,428,233,430,235,433,434,237,391,436,240, 438,242,440,255,244,444,246,247,334,248,249,406,250,455,251,458,253,254,463,464,346,257,468,258,259, 351,261,262,354,264,356,475,358,359,267,269,362,270,364,365,366,273,483,484,485,486,372,488,490,492, 280,281,378,282,380,283,501,383,456,503,286,387,388,389,288,323,508,393,511,291,514,397,424,516,517, 519,296,298,523,524,337,407,527,528,410,303,532,413,534,415,472,417,418,309,310,311,542,312,398,313, 426,314,316,429,318,549,550,320,321,453,324,554,326,558,328,441,561,443,331,563,540,447,448,566,450, 451,567,435,569,339,384,574,341,459,578,580,462,344,345,586,587,467,348,592,470,593,416,473,568,357, 515,597,599,600,601,481,603,368,369,370,371,512,373,489,374,491,375,493,494,495,612,584,498,614,500, 382,615,385,504,571,619,596,392,624,510,394,487,628,396,476,399,400,632,401,635,521,637,404,405,640, 535,408,409,533,530,644,412,529,414,526,647,537,538,649,446,650,422,646,544,545,654,606,656,431,432, 551,660,553,437,663,664,652,439,559,560,442,562,445,570,668,449,452,474,454,564,505,617,677,457,680, 681,669,460,579,461,581,670,684,497,585,465,466,687,659,683,689,469,471,626,595,507,477,610,478,479, 480,697,482,695,696,547,682,655,701,598,611,496,700,499,502,702,572,618,506,620,621,673,686,509,688, 594,642,513,629,630,631,518,712,634,520,704,522,638,718,525,641,627,720,531,645,543,536,690,539,541, 667,557,727,546,608,548,728,658,589,552,730,724,555,556,665,666,651,565,577,582,736,672,622,674,675, 676,573,678,679,575,576,607,590,583,685,623,588,625,591,648,691,692,746,711,604,605,602,698,699,613, 609,616,749,636,705,743,707,708,709,710,694,633,713,714,745,716,717,639,719,643,721,741,723,662,725, 726,653,657,729,661,748,752,744,734,735,671,737,738,739,740,722,742,706,733,715,693,747,731,703,750, 751,732,753,754,755,756] ,\[ 2,5,1,8,11,12,3,16,4,18,7,21,6,19,25,28,9,31,10,32,35,26,13,14,40, 15,41,17,43,45,24,47,20,49,23,22,52,54,56,36,60,27,62,29,65,30,68,33,70,34, 72,74,37,77,38,80,39,82,84,87,42,90,44,92,95,46,97,48,99,102,50,104,51,107,108, 53,112,93,55,116,57,119,58,123,59,126,61,129,131,63,134,137,64,139,66,141,144,67,148,69, 151,71,132,156,73,158,76,162,75,165,167,79,78,170,172,81,147,176,138,178,83,180,183,184,85, 187,86,189,191,88,194,89,195,198,91,200,113,121,204,94,207,96,209,212,155,98,215,216,217,100, 220,101,196,103,225,105,227,229,106,230,185,233,234,109,237,110,240,111,242,244,114,247,115,249,117, 252,118,254,120,257,122,259,125,261,124,262,264,127,267,128,268,130,269,154,273,133,246,276,135,169, 136,281,219,221,285,140,288,142,291,143,245,146,145,159,298,150,301,149,304,306,206,152,153,270,310, 311,313,157,297,182,160,161,164,318,163,190,323,263,166,326,168,280,328,197,331,171,334,173,337,174, 175,341,177,344,179,345,348,181,316,327,232,354,186,188,356,358,321,192,362,193,364,365,223,368,370, 199,371,373,317,201,378,202,203,383,385,205,388,208,391,393,396,397,210,211,400,213,214,251,404,406, 408,409,218,412,413,222,415,417,224,296,422,226,426,228,359,231,429,431,346,235,236,435,239,238,437, 241,439,441,243,443,445,446,360,248,449,450,452,453,250,456,253,459,461,255,465,256,466,258,447,414, 260,389,472,324,325,275,265,271,266,477,478,309,479,315,481,272,386,335,274,476,434,277,489,278,279, 494,496,498,499,282,500,283,430,284,504,495,286,330,287,505,507,289,510,290,513,293,515,292,294,518, 295,520,521,395,299,381,300,303,529,302,401,382,533,305,322,307,536,308,538,457,541,543,544,312,369, 314,545,427,547,548,320,319,551,553,535,473,555,556,559,367,560,329,352,398,399,564,332,333,425,361, 336,339,568,338,571,573,340,575,577,342,581,343,583,584,432,588,347,590,349,350,351,594,353,355,421, 357,598,524,492,363,602,366,527,605,436,567,372,607,609,610,374,611,375,440,376,379,377,380,613,526, 597,384,616,387,618,390,621,622,392,625,626,394,525,484,562,630,539,531,633,636,402,403,638,451,405, 407,641,642,643,410,411,645,470,593,416,648,418,423,419,420,615,651,424,517,653,428,493,502,657,658, 659,433,487,623,595,665,438,480,471,442,667,444,647,469,448,669,671,672,673,454,675,455,540,678,463, 458,640,683,460,664,632,462,682,654,464,591,685,688,467,549,468,680,690,485,474,475,614,565,692,694, 696,482,501,483,699,486,490,488,491,700,558,617,497,550,691,561,503,703,578,506,509,705,508,706,512, 528,511,708,514,532,516,582,624,519,714,522,715,717,523,579,719,707,530,721,711,534,585,537,693,674, 725,542,655,563,546,679,586,603,720,686,552,554,639,704,732,557,612,718,734,566,687,570,737,569,738, 572,712,592,574,656,736,576,580,740,742,587,697,589,743,730,596,745,599,601,600,747,606,604,710,608, 716,748,620,619,662,713,627,644,628,629,631,727,634,701,635,637,731,677,698,661,750,646,649,650,751, 652,733,744,660,722,663,666,668,746,670,753,724,676,681,752,684,729,702,689,723,735,695,728,739,709, 726,756,755,741,749,754] >; print "Group G is 32.U4(3):D8 < Sym(756)";