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Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1120 points:
(2,6,4,3)(5,15,9,8)(7,11,13,12)(10,28,18,17)(14,24,22,21)(16,20,26,25)(19,45,31,30)(23,41,35,34)(27,37,39,38)(29,33,43,42)(32,66,48,47)(36,62,52,51)(40,58,56,55)(44,54,60,59)(46,50,64,63)(49,91,69,68)(53,87,73,72)(57,83,77,76)(61,79,81,80)(65,75,85,84)(67,71,89,88)(70,120,94,93)(74,116,98,97)(78,112,102,101)(82,108,106,105)(86,104,110,109)(90,100,114,113)(92,96,118,117)(95,153,123,122)(99,149,127,126)(103,145,131,130)(107,141,135,134)(111,137,139,138)(115,133,143,142)(119,129,147,146)(121,125,151,150)(124,190,156,155)(128,186,160,159)(132,182,164,163)(136,178,168,167)(140,174,172,171)(144,170,176,175)(148,166,180,179)(152,162,184,183)(154,158,188,187)(157,231,193,192)(161,227,197,196)(165,223,201,200)(169,219,205,204)(173,215,209,208)(177,211,213,212)(181,207,217,216)(185,203,221,220)(189,199,225,224)(191,195,229,228)(194,276,234,233)(198,272,238,237)(202,268,242,241)(206,264,246,245)(210,260,250,249)(214,256,254,253)(218,252,258,257)(222,248,262,261)(226,244,266,265)(230,240,270,269)(232,236,274,273)(235,325,279,278)(239,321,283,282)(243,317,287,286)(247,313,291,290)(251,309,295,294)(255,305,299,298)(259,301,303,302)(263,297,307,306)(267,293,311,310)(271,289,315,314)(275,285,319,318)(277,281,323,322)(280,378,328,327)(284,374,332,331)(288,370,336,335)(292,366,340,339)(296,362,344,343)(300,358,348,347)(304,354,352,351)(308,350,356,355)(312,346,360,359)(316,342,364,363)(320,338,368,367)(324,334,372,371)(326,330,376,375)(329,435,381,380)(333,431,385,384)(337,427,389,388)(341,423,393,392)(345,419,397,396)(349,415,401,400)(353,411,405,404)(357,407,409,408)(361,403,413,412)(365,399,417,416)(369,395,421,420)(373,391,425,424)(377,387,429,428)(379,383,433,432)(382,496,438,437)(386,492,442,441)(390,488,446,445)(394,484,450,449)(398,480,454,453)(402,476,458,457)(406,472,462,461)(410,468,466,465)(414,464,470,469)(418,460,474,473)(422,456,478,477)(426,452,482,481)(430,448,486,485)(434,444,490,489)(436,440,494,493)(439,561,499,498)(443,557,503,502)(447,553,507,506)(451,549,511,510)(455,545,515,514)(459,541,519,518)(463,537,523,522)(467,533,527,526)(471,529,531,530)(475,525,535,534)(479,521,539,538)(483,517,543,542)(487,513,547,546)(491,509,551,550)(495,505,555,554)(497,501,559,558)(500,630,564,563)(504,626,568,567)(508,622,572,571)(512,618,576,575)(516,614,580,579)(520,610,584,583)(524,606,588,587)(528,602,592,591)(532,598,596,595)(536,594,600,599)(540,590,604,603)(544,586,608,607)(548,582,612,611)(552,578,616,615)(556,574,620,619)(560,570,624,623)(562,566,628,627)(565,703,633,632)(569,699,637,636)(573,695,641,640)(577,691,645,644)(581,687,649,648)(585,683,653,652)(589,679,657,656)(593,675,661,660)(597,671,665,664)(601,667,669,668)(605,663,673,672)(609,659,677,676)(613,655,681,680)(617,651,685,684)(621,647,689,688)(625,643,693,692)(629,639,697,696)(631,635,701,700)(634,780,706,705)(638,776,710,709)(642,772,714,713)(646,768,718,717)(650,764,722,721)(654,760,726,725)(658,756,730,729)(662,752,734,733)(666,748,738,737)(670,744,742,741)(674,740,746,745)(678,736,750,749)(682,732,754,753)(686,728,758,757)(690,724,762,761)(694,720,766,765)(698,716,770,769)(702,712,774,773)(704,708,778,777)(707,861,783,782)(711,857,787,786)(715,853,791,790)(719,849,795,794)(723,845,799,798)(727,841,803,802)(731,837,807,806)(735,833,811,810)(739,829,815,814)(743,825,819,818)(747,821,823,822)(751,817,827,826)(755,813,831,830)(759,809,835,834)(763,805,839,838)(767,801,843,842)(771,797,847,846)(775,793,851,850)(779,789,855,854)(781,785,859,858)(784,946,864,863)(788,942,868,867)(792,938,872,871)(796,934,876,875)(800,930,880,879)(804,926,884,883)(808,922,888,887)(812,918,892,891)(816,914,896,895)(820,910,900,899)(824,906,904,903)(828,902,908,907)(832,898,912,911)(836,894,916,915)(840,890,920,919)(844,886,924,923)(848,882,928,927)(852,878,932,931)(856,874,936,935)(860,870,940,939)(862,866,944,943)(865,1035,949,948)(869,1031,953,952)(873,1027,957,956)(877,1023,961,960)(881,1019,965,964)(885,1015,969,968)(889,1011,973,972)(893,1007,977,976)(897,1003,981,980)(901,999,985,984)(905,995,989,988)(909,991,993,992)(913,987,997,996)(917,983,1001,1000)(921,979,1005,1004)(925,975,1009,1008)(929,971,1013,1012)(933,967,1017,1016)(937,963,1021,1020)(941,959,1025,1024)(945,955,1029,1028)(947,951,1033,1032)(950,1050,1038,1037)(954,1106,1042,1041)(958,1104,1045,1039)(962,1102,1049,1048)(966,1100,1053,1052)(970,1098,1057,1056)(974,1096,1061,1060)(978,1094,1065,1064)(982,1092,1069,1068)(986,1090,1073,1072)(990,1087,1077,1076)(994,1083,1081,1080)(998,1079,1085,1084)(1002,1075,1089,1088)(1006,1071,1086,1091)(1010,1067,1082,1093)(1014,1063,1078,1095)(1018,1059,1074,1097)(1022,1055,1070,1099)(1026,1051,1066,1101)(1030,1047,1062,1103)(1034,1044,1058,1105)(1036,1040,1054,1107)(1043,1113,1109,1108)(1046,1114,1111,1110)(1112,1117,1116,1115)(1118,1119,1120);(1,2,5,10,19,32,49,70,95,124,157,194,235,280,329,382,439,500,565,634,707,784,865,950,1039,952,863,947,1034,1057,969,884,803,726,653,584,519,458,401,348,299,254,213,176,143,114,89,66,87,112,141,174,211,252,297,346,399,456,517,582,651,724,801,882,967,1055,1064,972,883,798,717,640,567,498,562,629,698,771,848,929,1014,1077,989,904,823,746,673,604,539,478,421,368,319,274,231,272,317,366,419,476,537,602,671,744,821,902,987,1075,1084,992,903,818,737,660,587,518,453,392,335,282,233,277,324,373,426,483,544,609,678,751,828,909,994,1082,1009,924,843,766,693,624,559,496,557,622,691,764,841,922,1007,1092,1097,1012,923,838,757,680,607,538,473,412,355,302,253,208,167,130,97,68,92,119,148,181,218,259,304,353,406,463,524,589,658,731,808,889,974,1062,1029,944,861,942,1027,1102,1107,1032,943,858,777,700,627,558,493,432,375,322,273,228,187,150,117,88,63,42,25,12,3,7,14,23,36,53,74,99,128,161,198,239,284,333,386,443,504,569,638,711,788,869,954,1043,1110,1041,948,1036,1053,965,880,799,722,649,580,515,454,397,344,295,250,209,172,139,110,85,64,45,62,83,108,137,170,207,248,293,342,395,452,513,578,647,720,797,878,963,1051,1060,968,879,794,713,636,563,631,702,775,852,933,1018,1073,985,900,819,742,669,600,535,474,417,364,315,270,229,190,227,268,313,362,415,472,533,598,667,740,817,898,983,1071,1080,988,899,814,733,656,583,514,449,388,331,278,326,377,430,487,548,613,682,755,832,913,998,1086,1005,920,839,762,689,620,555,494,435,492,553,618,687,760,837,918,1003,1090,1095,1008,919,834,753,676,603,534,469,408,351,298,249,204,163,126,93,121,152,185,222,263,308,357,410,467,528,593,662,735,812,893,978,1066,1025,940,859,780,857,938,1023,1100,1105,1028,939,854,773,696,623,554,489,428,371,318,269,224,183,146,113,84,59,38,21,8,16,27,40,57,78,103,132,165,202,243,288,337,390,447,508,573,642,715,792,873,958,1046,1112,1115,1108,1037,1049,961,876,795,718,645,576,511,450,393,340,291,246,205,168,135,106,81,60,43,28,41,58,79,104,133,166,203,244,289,338,391,448,509,574,643,716,793,874,959,1047,1056,964,875,790,709,632,704,779,856,937,1022,1069,981,896,815,738,665,596,531,470,413,360,311,266,225,188,153,186,223,264,309,358,411,468,529,594,663,736,813,894,979,1067,1076,984,895,810,729,652,579,510,445,384,327,379,434,491,552,617,686,759,836,917,1002,1089,1001,916,835,758,685,616,551,490,433,378,431,488,549,614,683,756,833,914,999,1087,1093,1004,915,830,749,672,599,530,465,404,347,294,245,200,159,122,154,189,226,267,312,361,414,471,532,597,666,739,816,897,982,1070,1021,936,855,778,703,776,853,934,1019,1098,1103,1024,935,850,769,692,619,550,485,424,367,314,265,220,179,142,109,80,55,34,17,29,44,61,82,107,136,169,206,247,292,341,394,451,512,577,646,719,796,877,962,1050,1113,1117,1116,1111,1045,957,872,791,714,641,572,507,446,389,336,287,242,201,164,131,102,77,56,39,26,15,24,37,54,75,100,129,162,199,240,285,334,387,444,505,570,639,712,789,870,955,1044,1052,960,871,786,705,781,860,941,1026,1065,977,892,811,734,661,592,527,466,409,356,307,262,221,184,151,120,149,182,219,260,305,354,407,464,525,590,659,732,809,890,975,1063,1072,980,891,806,725,648,575,506,441,380,436,495,556,621,690,763,840,921,1006,1085,997,912,831,754,681,612,547,486,429,376,325,374,427,484,545,610,679,752,829,910,995,1083,1091,1000,911,826,745,668,595,526,461,400,343,290,241,196,155,191,230,271,316,365,418,475,536,601,670,743,820,901,986,1074,1017,932,851,774,701,630,699,772,849,930,1015,1096,1101,1020,931,846,765,688,615,546,481,420,363,310,261,216,175,138,105,76,51,30,46,65,86,111,140,173,210,251,296,345,398,455,516,581,650,723,800,881,966,1054,1035,1106,1114,1109,1042,953,868,787,710,637,568,503,442,385,332,283,238,197,160,127,98,73,52,35,22,13,6,11,20,33,50,71,96,125,158,195,236,281,330,383,440,501,566,635,708,785,866,951,1040,1048,956,867,782,862,945,1030,1061,973,888,807,730,657,588,523,462,405,352,303,258,217,180,147,118,91,116,145,178,215,256,301,350,403,460,521,586,655,728,805,886,971,1059,1068,976,887,802,721,644,571,502,437,497,560,625,694,767,844,925,1010,1081,993,908,827,750,677,608,543,482,425,372,323,276,321,370,423,480,541,606,675,748,825,906,991,1079,1088,996,907,822,741,664,591,522,457,396,339,286,237,192,232,275,320,369,422,479,540,605,674,747,824,905,990,1078,1013,928,847,770,697,628,561,626,695,768,845,926,1011,1094,1099,1016,927,842,761,684,611,542,477,416,359,306,257,212,171,134,101,72,47,67,90,115,144,177,214,255,300,349,402,459,520,585,654,727,804,885,970,1058,1033,946,1031,1104,1038,949,864,783,706,633,564,499,438,381,328,279,234,193,156,123,94,69,48,31,18,9,4)
Conjugacy classes & character table
849 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13404, 10);
Finite Group Databasebeta