/*
www-ATLAS of Group Representations.
32.U4(3):D8 represented as permutations on 756 points.
*/

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