/*
www-ATLAS of Group Representations.
32.U4(3):D8 represented as permutations on 972 points.
*/

G<x,y>:=PermutationGroup<972|\[
2,1,5,7,3,10,4,12,14,6,17,8,20,9,23,25,11,28,30,13,33,35,15,38,16,
41,43,18,46,19,49,51,21,54,22,48,57,24,60,62,26,65,27,67,69,29,72,36,31,76,
32,79,80,34,83,85,37,88,90,39,93,40,95,97,42,100,44,103,45,105,107,47,110,111,113,
50,116,118,52,53,122,124,55,127,56,130,132,58,135,59,138,140,61,143,63,146,64,149,151,66,
131,154,68,157,70,160,71,163,165,73,74,169,75,172,174,77,177,78,179,180,182,81,184,82,187,
189,84,192,194,86,101,87,198,200,89,203,205,91,208,92,211,213,94,215,217,96,220,222,98,225,
99,227,229,102,232,234,104,236,237,106,240,242,108,245,109,248,250,252,112,243,256,114,259,115,262,
264,117,267,119,120,271,121,273,123,276,277,125,279,126,281,283,128,286,129,288,290,280,133,294,134,
297,299,136,302,137,304,306,139,309,311,141,314,142,266,144,319,145,322,323,147,325,148,327,328,150,
331,152,334,153,265,338,155,340,156,342,158,159,346,348,161,318,162,170,352,164,355,357,166,360,167,
363,168,366,367,368,171,370,372,173,375,376,175,378,176,230,214,178,384,385,387,181,389,183,392,394,
185,186,398,188,197,190,402,191,404,406,193,409,195,411,196,380,415,417,199,419,421,201,423,202,426,
408,204,429,206,431,207,434,435,209,396,210,437,438,212,441,344,443,241,216,446,420,218,219,450,221,
453,223,224,455,457,226,460,354,228,462,343,463,231,373,233,451,235,336,316,471,238,472,239,475,476,
477,244,480,333,246,484,247,486,487,249,481,490,251,493,495,253,254,255,467,257,499,258,339,502,260,
261,505,263,507,291,510,512,513,268,269,515,270,518,272,449,521,274,524,275,526,310,528,278,531,533,
534,282,537,284,539,285,542,301,287,545,289,547,468,550,292,552,293,554,295,321,296,556,298,558,560,
300,562,563,303,565,305,567,568,307,308,546,312,313,573,575,315,576,317,578,580,320,583,496,390,324,
341,588,326,590,329,593,330,595,488,332,597,335,337,601,603,605,369,413,608,609,345,347,613,615,349,
350,351,616,620,353,361,508,520,356,617,358,359,459,624,362,626,628,364,586,365,448,633,519,371,506,
637,374,640,642,377,500,379,482,600,381,648,382,383,652,386,655,656,388,498,483,391,649,658,393,621,
395,643,397,661,663,399,665,400,401,669,634,403,671,405,674,676,407,679,681,410,436,412,683,684,414,
686,416,689,418,692,422,695,424,690,425,607,427,428,699,430,702,432,433,704,622,707,708,439,711,440,
442,710,444,715,445,717,718,447,714,700,494,641,452,705,454,725,727,456,730,458,733,461,706,735,509,
464,737,465,685,466,610,561,469,470,606,743,745,473,747,474,478,485,667,673,479,525,570,721,489,752,
491,755,492,701,758,760,761,497,536,651,765,501,766,768,503,587,504,527,771,731,773,775,511,522,778,
635,514,668,782,516,517,756,523,741,696,529,788,530,672,532,791,618,653,535,795,538,664,619,540,798,
541,800,802,543,805,544,807,548,549,604,551,732,810,553,559,812,555,763,786,557,660,817,818,564,585,
629,566,820,569,589,598,571,572,826,577,574,769,824,584,579,831,581,582,834,835,623,813,827,836,591,
838,592,753,840,594,645,687,596,792,599,844,602,846,804,848,659,850,611,853,612,856,614,857,849,843,
774,625,728,860,627,657,864,630,816,631,632,767,693,865,636,638,762,639,712,871,644,872,646,751,647,
875,876,650,821,868,878,654,806,880,881,694,883,662,815,859,666,734,886,887,670,889,885,675,891,677,
893,678,894,739,680,783,682,873,897,688,899,691,722,888,789,759,697,698,902,703,779,905,906,713,854,
709,723,863,832,908,716,829,910,719,720,724,855,726,862,729,912,914,750,736,915,738,851,740,749,742,
847,917,744,825,837,746,748,921,790,754,923,839,828,757,764,918,869,780,867,924,770,772,808,929,776,
777,925,781,932,784,785,935,787,937,797,793,794,814,796,940,799,941,801,803,922,943,809,944,811,946,
933,819,931,948,822,823,930,830,950,833,927,841,916,842,845,913,852,866,953,955,858,895,861,870,877,
958,911,959,874,907,903,879,901,961,882,962,884,939,938,890,892,956,896,898,964,900,957,904,963,909,
965,966,919,967,920,942,947,926,928,970,934,936,949,945,951,952,954,971,972,960,968,969]
,\[
3,4,6,8,9,1,11,13,15,16,18,19,21,22,24,26,27,29,31,32,34,36,37,39,40,
42,44,45,47,48,50,52,53,2,55,56,58,59,61,63,64,66,54,68,70,71,73,74,75,77,
78,20,81,82,84,86,87,89,91,92,5,94,96,98,99,101,102,104,93,106,108,109,7,112,114,
115,117,119,120,121,123,125,126,128,129,131,133,134,136,137,139,141,142,144,145,147,148,150,152,153,
10,155,156,158,159,161,162,164,166,167,168,170,171,173,175,176,12,178,95,181,177,183,185,186,188,
190,191,193,195,196,14,197,199,201,202,204,206,207,209,210,212,214,43,216,218,219,221,223,224,226,
49,228,230,231,233,157,235,17,238,239,241,243,244,246,247,249,251,253,254,255,257,258,260,261,263,
265,266,268,269,270,272,264,274,275,194,278,208,143,280,282,284,285,287,33,289,291,292,293,295,296,
298,300,301,23,303,305,307,308,310,312,313,315,316,317,318,320,321,51,324,80,25,326,184,329,330,
332,333,335,336,337,339,90,341,234,343,344,345,347,118,349,28,350,351,353,354,356,358,359,361,362,
364,365,288,113,30,369,371,373,374,151,327,377,379,380,381,382,383,294,386,322,388,390,391,393,395,
396,397,399,400,401,130,403,281,405,407,408,35,410,412,413,414,416,418,160,420,200,422,424,425,427,
122,428,430,65,432,433,140,436,402,38,355,138,439,440,378,442,389,444,445,346,447,448,449,451,452,
262,273,454,456,458,459,41,461,72,304,302,297,464,465,466,467,468,469,470,237,62,473,474,179,189,
478,479,481,482,483,46,485,198,488,489,334,491,492,494,227,496,314,497,325,498,169,500,501,503,504,
453,506,60,508,509,511,220,514,460,443,516,517,519,69,520,522,523,203,525,97,527,529,530,532,267,
535,536,495,538,540,541,543,182,544,546,534,548,549,283,551,553,187,165,555,57,406,100,557,559,561,
426,463,387,564,205,566,232,484,569,570,487,571,572,574,225,505,577,348,579,581,582,507,584,585,586,
587,589,376,591,592,594,547,367,211,596,598,599,600,602,604,606,67,607,103,610,611,612,614,609,616,
617,618,619,621,622,437,438,623,450,556,404,417,248,368,625,627,629,630,631,83,632,634,539,635,636,
638,639,641,643,644,645,646,76,286,647,649,650,651,653,654,240,229,545,526,79,657,174,648,510,513,
659,502,660,662,533,664,666,667,668,242,352,670,672,673,675,677,678,680,290,624,111,682,85,685,192,
687,688,690,691,693,694,696,697,88,542,603,299,698,700,701,236,338,703,705,706,163,709,710,331,328,
712,713,714,716,655,323,311,340,719,319,720,721,722,723,724,726,728,729,731,732,734,620,252,384,135,
736,738,739,608,740,741,742,154,663,431,744,746,628,105,748,565,423,749,107,671,309,750,446,751,753,
754,756,707,757,759,110,762,763,683,764,695,737,767,769,770,615,583,375,772,222,774,776,777,116,779,
780,781,279,717,518,783,784,785,786,787,366,789,385,493,790,124,792,793,794,537,745,796,797,773,127,
799,801,803,804,550,806,808,360,809,409,476,480,811,372,132,813,814,810,815,816,686,771,819,820,821,
822,342,499,823,824,652,825,661,245,827,394,457,828,829,830,832,833,357,180,306,146,455,256,837,626,
839,725,791,841,842,149,843,434,462,435,831,845,847,562,849,642,851,852,854,855,838,704,259,758,415,
580,858,859,861,862,863,656,826,865,866,867,708,868,848,768,869,172,870,276,715,800,755,873,217,874,
860,877,475,512,711,735,879,363,554,882,271,788,818,884,563,588,885,699,883,888,798,890,486,892,730,
805,872,895,896,421,490,477,576,898,760,864,900,521,552,718,689,601,901,903,411,904,778,590,907,878,
807,573,213,578,846,909,215,911,633,886,856,747,876,575,679,913,558,595,908,916,914,567,568,605,765,
702,918,887,919,889,920,817,752,681,922,875,441,250,692,531,419,880,924,925,926,927,593,928,840,727,
930,906,931,933,934,893,936,795,277,398,674,938,939,597,370,658,676,897,929,942,775,881,921,945,947,
528,429,665,902,910,392,733,949,857,761,951,637,802,640,850,952,812,743,954,956,955,524,923,957,946,
915,950,835,935,472,613,853,960,905,844,963,961,953,669,871,684,560,944,836,782,958,965,917,894,959,
515,912,964,471,941,943,834,968,969,899,967,971,891,932,948,966,937,766,940,972,962,970]
>;
print "Group G is 32.U4(3):D8 < Sym(972)";