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Dic7819 #44530810
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1128 points:
(1,2)(3,4)(5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128);(1,3,2,4)(6,11)(7,10)(8,9)(13,1128)(14,1127)(15,1126)(16,1125)(17,1124)(18,1123)(19,1122)(20,1121)(21,1120)(22,1119)(23,1118)(24,1117)(25,1116)(26,1115)(27,1114)(28,1113)(29,1112)(30,1111)(31,1110)(32,1109)(33,1108)(34,1107)(35,1106)(36,1105)(37,1104)(38,1103)(39,1102)(40,1101)(41,1100)(42,1099)(43,1098)(44,1097)(45,1096)(46,1095)(47,1094)(48,1093)(49,1092)(50,1091)(51,1090)(52,1089)(53,1088)(54,1087)(55,1086)(56,1085)(57,1084)(58,1083)(59,1082)(60,1081)(61,1080)(62,1079)(63,1078)(64,1077)(65,1076)(66,1075)(67,1074)(68,1073)(69,1072)(70,1071)(71,1070)(72,1069)(73,1068)(74,1067)(75,1066)(76,1065)(77,1064)(78,1063)(79,1062)(80,1061)(81,1060)(82,1059)(83,1058)(84,1057)(85,1056)(86,1055)(87,1054)(88,1053)(89,1052)(90,1051)(91,1050)(92,1049)(93,1048)(94,1047)(95,1046)(96,1045)(97,1044)(98,1043)(99,1042)(100,1041)(101,1040)(102,1039)(103,1038)(104,1037)(105,1036)(106,1035)(107,1034)(108,1033)(109,1032)(110,1031)(111,1030)(112,1029)(113,1028)(114,1027)(115,1026)(116,1025)(117,1024)(118,1023)(119,1022)(120,1021)(121,1020)(122,1019)(123,1018)(124,1017)(125,1016)(126,1015)(127,1014)(128,1013)(129,1012)(130,1011)(131,1010)(132,1009)(133,1008)(134,1007)(135,1006)(136,1005)(137,1004)(138,1003)(139,1002)(140,1001)(141,1000)(142,999)(143,998)(144,997)(145,996)(146,995)(147,994)(148,993)(149,992)(150,991)(151,990)(152,989)(153,988)(154,987)(155,986)(156,985)(157,984)(158,983)(159,982)(160,981)(161,980)(162,979)(163,978)(164,977)(165,976)(166,975)(167,974)(168,973)(169,972)(170,971)(171,970)(172,969)(173,968)(174,967)(175,966)(176,965)(177,964)(178,963)(179,962)(180,961)(181,960)(182,959)(183,958)(184,957)(185,956)(186,955)(187,954)(188,953)(189,952)(190,951)(191,950)(192,949)(193,948)(194,947)(195,946)(196,945)(197,944)(198,943)(199,942)(200,941)(201,940)(202,939)(203,938)(204,937)(205,936)(206,935)(207,934)(208,933)(209,932)(210,931)(211,930)(212,929)(213,928)(214,927)(215,926)(216,925)(217,924)(218,923)(219,922)(220,921)(221,920)(222,919)(223,918)(224,917)(225,916)(226,915)(227,914)(228,913)(229,912)(230,911)(231,910)(232,909)(233,908)(234,907)(235,906)(236,905)(237,904)(238,903)(239,902)(240,901)(241,900)(242,899)(243,898)(244,897)(245,896)(246,895)(247,894)(248,893)(249,892)(250,891)(251,890)(252,889)(253,888)(254,887)(255,886)(256,885)(257,884)(258,883)(259,882)(260,881)(261,880)(262,879)(263,878)(264,877)(265,876)(266,875)(267,874)(268,873)(269,872)(270,871)(271,870)(272,869)(273,868)(274,867)(275,866)(276,865)(277,864)(278,863)(279,862)(280,861)(281,860)(282,859)(283,858)(284,857)(285,856)(286,855)(287,854)(288,853)(289,852)(290,851)(291,850)(292,849)(293,848)(294,847)(295,846)(296,845)(297,844)(298,843)(299,842)(300,841)(301,840)(302,839)(303,838)(304,837)(305,836)(306,835)(307,834)(308,833)(309,832)(310,831)(311,830)(312,829)(313,828)(314,827)(315,826)(316,825)(317,824)(318,823)(319,822)(320,821)(321,820)(322,819)(323,818)(324,817)(325,816)(326,815)(327,814)(328,813)(329,812)(330,811)(331,810)(332,809)(333,808)(334,807)(335,806)(336,805)(337,804)(338,803)(339,802)(340,801)(341,800)(342,799)(343,798)(344,797)(345,796)(346,795)(347,794)(348,793)(349,792)(350,791)(351,790)(352,789)(353,788)(354,787)(355,786)(356,785)(357,784)(358,783)(359,782)(360,781)(361,780)(362,779)(363,778)(364,777)(365,776)(366,775)(367,774)(368,773)(369,772)(370,771)(371,770)(372,769)(373,768)(374,767)(375,766)(376,765)(377,764)(378,763)(379,762)(380,761)(381,760)(382,759)(383,758)(384,757)(385,756)(386,755)(387,754)(388,753)(389,752)(390,751)(391,750)(392,749)(393,748)(394,747)(395,746)(396,745)(397,744)(398,743)(399,742)(400,741)(401,740)(402,739)(403,738)(404,737)(405,736)(406,735)(407,734)(408,733)(409,732)(410,731)(411,730)(412,729)(413,728)(414,727)(415,726)(416,725)(417,724)(418,723)(419,722)(420,721)(421,720)(422,719)(423,718)(424,717)(425,716)(426,715)(427,714)(428,713)(429,712)(430,711)(431,710)(432,709)(433,708)(434,707)(435,706)(436,705)(437,704)(438,703)(439,702)(440,701)(441,700)(442,699)(443,698)(444,697)(445,696)(446,695)(447,694)(448,693)(449,692)(450,691)(451,690)(452,689)(453,688)(454,687)(455,686)(456,685)(457,684)(458,683)(459,682)(460,681)(461,680)(462,679)(463,678)(464,677)(465,676)(466,675)(467,674)(468,673)(469,672)(470,671)(471,670)(472,669)(473,668)(474,667)(475,666)(476,665)(477,664)(478,663)(479,662)(480,661)(481,660)(482,659)(483,658)(484,657)(485,656)(486,655)(487,654)(488,653)(489,652)(490,651)(491,650)(492,649)(493,648)(494,647)(495,646)(496,645)(497,644)(498,643)(499,642)(500,641)(501,640)(502,639)(503,638)(504,637)(505,636)(506,635)(507,634)(508,633)(509,632)(510,631)(511,630)(512,629)(513,628)(514,627)(515,626)(516,625)(517,624)(518,623)(519,622)(520,621)(521,620)(522,619)(523,618)(524,617)(525,616)(526,615)(527,614)(528,613)(529,612)(530,611)(531,610)(532,609)(533,608)(534,607)(535,606)(536,605)(537,604)(538,603)(539,602)(540,601)(541,600)(542,599)(543,598)(544,597)(545,596)(546,595)(547,594)(548,593)(549,592)(550,591)(551,590)(552,589)(553,588)(554,587)(555,586)(556,585)(557,584)(558,583)(559,582)(560,581)(561,580)(562,579)(563,578)(564,577)(565,576)(566,575)(567,574)(568,573)(569,572)(570,571)
Polycyclic presentation:
2,7,1117,2|a^2=d,b^a=b^6,c^a=c^1116
Conjugacy classes & character table
7822 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31276, 4);
Finite Group Databasebeta