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Dic7903 #44539208
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1140 points:
(1,2)(3,4)(5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140);(1,3,2,4)(6,11)(7,10)(8,9)(13,1140)(14,1139)(15,1138)(16,1137)(17,1136)(18,1135)(19,1134)(20,1133)(21,1132)(22,1131)(23,1130)(24,1129)(25,1128)(26,1127)(27,1126)(28,1125)(29,1124)(30,1123)(31,1122)(32,1121)(33,1120)(34,1119)(35,1118)(36,1117)(37,1116)(38,1115)(39,1114)(40,1113)(41,1112)(42,1111)(43,1110)(44,1109)(45,1108)(46,1107)(47,1106)(48,1105)(49,1104)(50,1103)(51,1102)(52,1101)(53,1100)(54,1099)(55,1098)(56,1097)(57,1096)(58,1095)(59,1094)(60,1093)(61,1092)(62,1091)(63,1090)(64,1089)(65,1088)(66,1087)(67,1086)(68,1085)(69,1084)(70,1083)(71,1082)(72,1081)(73,1080)(74,1079)(75,1078)(76,1077)(77,1076)(78,1075)(79,1074)(80,1073)(81,1072)(82,1071)(83,1070)(84,1069)(85,1068)(86,1067)(87,1066)(88,1065)(89,1064)(90,1063)(91,1062)(92,1061)(93,1060)(94,1059)(95,1058)(96,1057)(97,1056)(98,1055)(99,1054)(100,1053)(101,1052)(102,1051)(103,1050)(104,1049)(105,1048)(106,1047)(107,1046)(108,1045)(109,1044)(110,1043)(111,1042)(112,1041)(113,1040)(114,1039)(115,1038)(116,1037)(117,1036)(118,1035)(119,1034)(120,1033)(121,1032)(122,1031)(123,1030)(124,1029)(125,1028)(126,1027)(127,1026)(128,1025)(129,1024)(130,1023)(131,1022)(132,1021)(133,1020)(134,1019)(135,1018)(136,1017)(137,1016)(138,1015)(139,1014)(140,1013)(141,1012)(142,1011)(143,1010)(144,1009)(145,1008)(146,1007)(147,1006)(148,1005)(149,1004)(150,1003)(151,1002)(152,1001)(153,1000)(154,999)(155,998)(156,997)(157,996)(158,995)(159,994)(160,993)(161,992)(162,991)(163,990)(164,989)(165,988)(166,987)(167,986)(168,985)(169,984)(170,983)(171,982)(172,981)(173,980)(174,979)(175,978)(176,977)(177,976)(178,975)(179,974)(180,973)(181,972)(182,971)(183,970)(184,969)(185,968)(186,967)(187,966)(188,965)(189,964)(190,963)(191,962)(192,961)(193,960)(194,959)(195,958)(196,957)(197,956)(198,955)(199,954)(200,953)(201,952)(202,951)(203,950)(204,949)(205,948)(206,947)(207,946)(208,945)(209,944)(210,943)(211,942)(212,941)(213,940)(214,939)(215,938)(216,937)(217,936)(218,935)(219,934)(220,933)(221,932)(222,931)(223,930)(224,929)(225,928)(226,927)(227,926)(228,925)(229,924)(230,923)(231,922)(232,921)(233,920)(234,919)(235,918)(236,917)(237,916)(238,915)(239,914)(240,913)(241,912)(242,911)(243,910)(244,909)(245,908)(246,907)(247,906)(248,905)(249,904)(250,903)(251,902)(252,901)(253,900)(254,899)(255,898)(256,897)(257,896)(258,895)(259,894)(260,893)(261,892)(262,891)(263,890)(264,889)(265,888)(266,887)(267,886)(268,885)(269,884)(270,883)(271,882)(272,881)(273,880)(274,879)(275,878)(276,877)(277,876)(278,875)(279,874)(280,873)(281,872)(282,871)(283,870)(284,869)(285,868)(286,867)(287,866)(288,865)(289,864)(290,863)(291,862)(292,861)(293,860)(294,859)(295,858)(296,857)(297,856)(298,855)(299,854)(300,853)(301,852)(302,851)(303,850)(304,849)(305,848)(306,847)(307,846)(308,845)(309,844)(310,843)(311,842)(312,841)(313,840)(314,839)(315,838)(316,837)(317,836)(318,835)(319,834)(320,833)(321,832)(322,831)(323,830)(324,829)(325,828)(326,827)(327,826)(328,825)(329,824)(330,823)(331,822)(332,821)(333,820)(334,819)(335,818)(336,817)(337,816)(338,815)(339,814)(340,813)(341,812)(342,811)(343,810)(344,809)(345,808)(346,807)(347,806)(348,805)(349,804)(350,803)(351,802)(352,801)(353,800)(354,799)(355,798)(356,797)(357,796)(358,795)(359,794)(360,793)(361,792)(362,791)(363,790)(364,789)(365,788)(366,787)(367,786)(368,785)(369,784)(370,783)(371,782)(372,781)(373,780)(374,779)(375,778)(376,777)(377,776)(378,775)(379,774)(380,773)(381,772)(382,771)(383,770)(384,769)(385,768)(386,767)(387,766)(388,765)(389,764)(390,763)(391,762)(392,761)(393,760)(394,759)(395,758)(396,757)(397,756)(398,755)(399,754)(400,753)(401,752)(402,751)(403,750)(404,749)(405,748)(406,747)(407,746)(408,745)(409,744)(410,743)(411,742)(412,741)(413,740)(414,739)(415,738)(416,737)(417,736)(418,735)(419,734)(420,733)(421,732)(422,731)(423,730)(424,729)(425,728)(426,727)(427,726)(428,725)(429,724)(430,723)(431,722)(432,721)(433,720)(434,719)(435,718)(436,717)(437,716)(438,715)(439,714)(440,713)(441,712)(442,711)(443,710)(444,709)(445,708)(446,707)(447,706)(448,705)(449,704)(450,703)(451,702)(452,701)(453,700)(454,699)(455,698)(456,697)(457,696)(458,695)(459,694)(460,693)(461,692)(462,691)(463,690)(464,689)(465,688)(466,687)(467,686)(468,685)(469,684)(470,683)(471,682)(472,681)(473,680)(474,679)(475,678)(476,677)(477,676)(478,675)(479,674)(480,673)(481,672)(482,671)(483,670)(484,669)(485,668)(486,667)(487,666)(488,665)(489,664)(490,663)(491,662)(492,661)(493,660)(494,659)(495,658)(496,657)(497,656)(498,655)(499,654)(500,653)(501,652)(502,651)(503,650)(504,649)(505,648)(506,647)(507,646)(508,645)(509,644)(510,643)(511,642)(512,641)(513,640)(514,639)(515,638)(516,637)(517,636)(518,635)(519,634)(520,633)(521,632)(522,631)(523,630)(524,629)(525,628)(526,627)(527,626)(528,625)(529,624)(530,623)(531,622)(532,621)(533,620)(534,619)(535,618)(536,617)(537,616)(538,615)(539,614)(540,613)(541,612)(542,611)(543,610)(544,609)(545,608)(546,607)(547,606)(548,605)(549,604)(550,603)(551,602)(552,601)(553,600)(554,599)(555,598)(556,597)(557,596)(558,595)(559,594)(560,593)(561,592)(562,591)(563,590)(564,589)(565,588)(566,587)(567,586)(568,585)(569,584)(570,583)(571,582)(572,581)(573,580)(574,579)(575,578)(576,577)
Polycyclic presentation:
2,7,1129,2|a^2=d,b^a=b^6,c^a=c^1128
Conjugacy classes & character table
7906 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31612, 4);
Finite Group Databasebeta