PermutationGroup<1134|
\[306,761,628,790,173,933,643,451,690,10,578,368,160,370,158,
871,887,543,652,60,1133,484,792,821,118,658,977,45,826,274,
948,1120,377,548,35,699,837,988,1084,926,303,824,603,895,28,
126,205,48,479,124,903,76,73,524,590,216,456,475,592,20,606,
390,816,139,817,841,794,1123,69,364,505,1087,53,1048,386,52,
831,230,455,904,326,741,1067,558,342,540,946,896,248,90,883,
651,250,290,249,708,188,362,612,769,806,746,343,715,649,133,
195,549,1128,742,111,872,911,114,363,482,329,25,359,915,539,
358,152,50,1012,46,698,1010,292,495,781,979,106,266,317,637,
607,283,64,547,960,371,1081,304,297,586,1061,148,797,566,728,
123,630,804,886,533,546,15,839,13,278,740,986,597,372,253,
793,560,323,927,610,172,5,964,1101,583,318,424,696,217,1064,
291,494,373,615,730,914,97,828,308,867,497,466,1054,107,751,
489,305,199,1082,426,231,203,459,47,616,710,638,786,210,731,
922,814,1038,244,56,180,321,621,855,918,276,675,732,984,307,
450,924,834,78,202,582,452,1018,261,925,574,618,293,1125,1016,
242,243,215,286,561,600,89,95,93,760,966,166,878,449,993,257,
437,856,311,235,262,801,1083,996,134,770,685,799,577,976,563,
692,30,393,222,991,161,654,519,503,1089,138,346,748,245,943,
858,598,94,182,129,239,412,727,1129,145,1056,680,863,1045,623,
41,144,198,1,226,190,485,992,260,989,973,703,1026,552,135,
177,516,994,218,1112,169,408,686,81,504,1121,117,838,877,735,
620,415,909,679,723,668,445,341,340,85,103,522,667,284,712,
663,423,526,880,413,487,537,640,750,520,122,119,1011,403,98,
115,70,764,910,472,12,1115,14,142,165,184,457,534,842,33,
1004,379,949,851,953,864,1092,588,75,1104,913,1053,62,502,480,
275,811,1127,471,464,942,481,634,743,1051,361,1059,762,836,
492,324,941,724,753,294,352,655,334,430,768,726,672,420,422,
421,349,178,596,201,573,788,765,416,431,773,1057,705,470,530,
258,1088,789,488,975,674,968,843,339,1015,521,857,255,227,8,
233,866,898,79,57,374,1085,204,906,518,937,815,397,609,193,
511,1111,662,435,396,367,709,602,58,755,683,673,49,392,399,
116,958,22,309,545,353,440,197,978,1052,407,1102,183,130,1124,
192,498,632,500,829,391,281,327,71,625,930,700,656,955,467,
1117,954,1079,897,319,738,461,280,357,447,344,523,54,624,350,
936,1058,1100,436,1034,532,156,375,1126,985,354,1105,121,86,
1033,737,18,882,486,157,140,34,108,983,1022,316,1040,846,756,
556,853,84,947,168,246,928,272,1046,1078,150,881,859,938,1113,
798,905,427,237,579,970,270,11,575,580,678,232,176,584,639,
146,1063,385,1095,55,684,59,1098,759,1062,425,164,289,736,247,
766,474,43,1001,1041,61,137,1116,465,171,611,99,647,1090,185,
206,665,238,899,333,219,653,302,525,506,1134,661,3,763,153,
934,499,1027,400,998,1039,136,208,585,355,1007,812,7,644,796,
657,613,1050,105,664,92,19,622,279,414,509,646,26,691,785,
627,469,348,650,617,1036,345,338,1025,695,707,419,478,442,223,
1000,852,581,336,299,875,1070,477,591,268,325,713,894,807,9,
659,273,778,827,670,179,961,127,36,508,813,892,314,1029,434,
729,671,96,473,207,840,347,687,1008,104,1103,912,718,874,720,
721,745,337,410,1049,418,295,151,706,186,211,224,733,734,332,
599,542,517,1069,162,82,110,401,744,722,102,754,285,803,356,
196,1075,411,747,476,555,1047,907,594,251,2,405,629,365,429,
601,850,417,100,267,1107,873,432,774,919,835,980,693,1020,916,
131,805,1131,982,660,209,787,428,439,4,844,23,167,67,1003,
645,149,571,269,800,263,917,749,154,782,101,689,1023,845,825,
394,642,701,213,463,63,65,995,990,884,24,987,1013,42,810,29,
694,189,501,876,77,969,833,229,776,406,37,330,159,711,66,376,
444,791,809,554,1035,1065,963,767,381,677,557,1024,220,259,
448,288,568,860,997,1042,300,383,865,453,191,868,869,931,16,
112,772,719,681,830,331,254,999,351,567,544,91,820,1060,155,
17,1109,1076,951,900,702,893,688,44,88,515,454,619,891,923,
1093,51,80,572,460,758,908,335,366,113,717,388,187,120,780,
802,221,775,920,1014,212,901,228,236,40,170,562,929,507,870,
1017,6,631,939,527,462,569,935,1037,409,398,287,1118,1122,87,
559,31,380,950,890,1043,382,513,510,1077,1044,483,1073,141,
697,965,849,174,962,252,1072,443,832,576,1132,1055,313,1106,
441,271,27,490,132,777,1091,784,550,225,536,163,822,38,312,
819,277,310,256,320,818,265,861,635,879,676,604,1119,795,378,
1019,1108,641,714,1009,128,360,125,823,921,446,241,932,234,
1005,779,1021,551,808,854,669,315,633,1074,704,1030,1066,1080,
541,531,847,666,940,214,636,553,605,862,952,957,301,564,757,
74,725,648,402,491,389,194,972,298,433,528,404,885,147,595,
587,181,848,1031,83,1130,739,682,1071,967,959,1028,752,889,
956,565,514,1032,143,200,264,39,458,1094,72,438,282,614,981,
384,902,1086,589,1099,1097,593,1096,529,175,493,716,387,538,
974,771,1006,888,1110,468,322,570,1114,369,608,512,944,1002,
32,328,945,68,496,240,535,395,109,296,1068,783,971,21,626],
\[540,557,21,483,167,1061,531,307,454,874,942,853,367,573,
419,250,96,377,867,849,1073,586,133,501,811,455,422,281,266,
552,339,1033,829,537,294,505,1050,434,825,437,370,34,608,609,
739,576,972,391,522,682,80,1083,790,893,1112,695,382,456,1004,
433,989,1068,1047,743,283,397,681,84,737,841,44,78,1098,896,
528,780,719,306,625,485,964,1058,353,449,141,520,539,658,945,
1110,417,526,151,62,1117,176,547,61,774,736,368,1121,559,19,
269,638,136,291,560,795,38,969,888,384,228,467,663,937,742,
1097,670,448,846,683,352,414,190,452,206,69,196,987,326,412,
120,380,47,762,329,886,611,974,857,103,100,910,1049,1114,1092,
633,918,1013,308,316,148,18,87,809,684,226,1074,1014,194,543,
182,1046,721,362,399,134,97,106,636,726,251,17,803,153,949,
443,118,490,302,400,626,423,1040,6,95,284,358,933,508,1101,
482,968,388,868,1009,1072,583,332,847,54,125,621,351,225,794,
1003,773,224,435,880,14,177,138,620,446,720,7,707,850,381,
582,760,614,472,37,667,786,578,333,511,924,662,1024,43,603,
855,143,371,735,1057,175,1130,300,1078,49,430,245,666,875,645,
9,1082,428,1060,898,1028,1089,643,407,729,525,535,550,76,799,
655,530,325,409,660,453,1128,187,8,598,692,615,64,807,127,
264,392,820,420,26,812,1125,613,650,651,596,259,1106,73,1122,
523,1077,669,263,994,184,72,278,178,1127,653,113,865,671,222,
200,1091,551,159,180,600,830,478,1039,445,570,23,152,599,904,
998,585,915,877,1042,826,89,529,939,1102,770,754,425,436,930,
999,728,1029,257,57,975,1096,205,383,581,295,859,796,950,378,
56,1055,961,1001,946,843,24,1123,821,1120,460,723,959,685,882,
734,906,156,480,977,107,212,349,83,1011,701,659,374,899,451,
77,618,958,432,674,686,411,932,312,595,305,779,536,288,907,
814,630,303,577,986,815,544,170,1133,632,484,828,441,694,617,
403,487,1059,624,365,1109,627,121,348,691,16,757,1023,827,111,
1043,1036,839,81,936,634,91,641,319,174,1006,816,1027,824,68,
1035,920,1100,938,255,289,891,179,195,495,41,840,86,211,109,
372,509,1063,702,1118,149,112,115,234,955,1015,261,99,1087,
331,359,1,458,1056,740,51,781,798,232,356,165,236,558,833,
901,976,67,271,677,885,158,366,792,394,173,894,79,801,777,
1020,474,473,354,401,616,426,244,214,745,724,462,1030,249,247,
320,758,665,604,549,566,497,221,402,842,1065,29,532,42,1104,
157,481,856,237,988,396,227,705,171,876,75,631,1115,793,1012,
447,782,710,954,791,144,464,287,1070,943,555,709,337,209,912,
345,272,439,124,215,628,800,732,908,488,235,768,512,208,966,
562,479,834,274,725,198,805,429,292,185,1071,169,355,386,746,
808,524,499,253,963,759,911,697,848,238,71,418,85,223,592,
545,28,1086,15,48,605,1119,129,1103,53,186,506,593,515,1005,
864,967,267,126,873,664,704,504,649,172,344,622,1021,997,971,
982,970,755,280,33,700,941,35,270,764,979,652,749,1032,712,
597,587,74,491,1002,440,92,751,881,50,183,427,902,276,90,503,
11,538,1022,788,698,708,496,668,572,318,822,787,771,1113,475,
357,591,647,431,610,360,1076,928,1026,835,637,965,838,926,
1067,1008,10,314,718,817,802,818,88,590,290,321,299,110,680,
390,804,5,12,242,866,1129,444,917,772,285,1093,957,46,533,
810,750,145,130,246,863,415,55,878,282,871,1054,279,59,1031,
1132,243,252,256,851,921,858,369,693,265,527,160,301,217,696,
310,654,870,469,1111,744,897,1084,346,463,477,405,502,193,688,
513,268,947,564,39,364,541,813,395,832,258,623,492,776,30,
567,717,690,629,421,105,922,1064,556,216,220,713,534,65,328,
500,375,919,714,231,775,1107,219,565,1090,703,561,101,373,240,
122,783,927,60,1116,648,715,1025,678,1081,22,978,1053,892,468,
40,983,845,733,424,82,70,1034,992,862,900,612,991,260,722,
494,823,785,241,646,489,553,52,607,45,797,398,519,104,589,
766,869,769,903,150,706,602,1126,233,119,1131,517,230,387,642,
914,601,1018,450,311,521,248,58,1007,204,36,323,661,340,296,
197,20,854,313,984,139,1066,923,1017,408,644,1041,619,973,727,
1124,202,1080,913,93,25,389,341,575,376,579,948,819,335,606,
297,639,1075,66,980,199,309,571,181,275,1079,657,293,675,951,
831,336,784,486,1108,457,191,563,350,730,2,510,594,1048,286,
465,132,168,32,239,438,385,201,406,131,471,254,262,137,568,
1044,952,459,990,699,765,192,147,909,461,872,879,273,960,164,
98,379,753,203,210,1085,102,161,883,1062,569,162,1016,117,993,
747,574,324,837,546,934,63,114,860,327,1000,689,363,404,140,
361,466,442,498,393,542,944,679,554,852,1099,889,1134,940,962,
123,887,343,166,1095,895,277,146,1051,213,142,836,1037,1010,
731,981,229,334,905,1045,518,1019,4,516,844,27,789,188,330,
116,507,806,1052,635,94,413,584,956,315,3,996,1105,763,761,
890,338,1088,493,752,861,687,304,514,322,916,476,711,154,470,
953,1038,1094,207,135,298,347,128,163,31,640,676,931,929,410,
925,342,673,580,741,778,155,317,416,189,767,218,756,995,716,
13,884,108,548,935,672,588,738,985,656,1069,748]
/*order=12737088=2^6*3^7*7*13*/>
