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D12881 #38788460
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1182 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182);(2,11)(3,10)(4,9)(5,8)(6,7)(13,1182)(14,1181)(15,1180)(16,1179)(17,1178)(18,1177)(19,1176)(20,1175)(21,1174)(22,1173)(23,1172)(24,1171)(25,1170)(26,1169)(27,1168)(28,1167)(29,1166)(30,1165)(31,1164)(32,1163)(33,1162)(34,1161)(35,1160)(36,1159)(37,1158)(38,1157)(39,1156)(40,1155)(41,1154)(42,1153)(43,1152)(44,1151)(45,1150)(46,1149)(47,1148)(48,1147)(49,1146)(50,1145)(51,1144)(52,1143)(53,1142)(54,1141)(55,1140)(56,1139)(57,1138)(58,1137)(59,1136)(60,1135)(61,1134)(62,1133)(63,1132)(64,1131)(65,1130)(66,1129)(67,1128)(68,1127)(69,1126)(70,1125)(71,1124)(72,1123)(73,1122)(74,1121)(75,1120)(76,1119)(77,1118)(78,1117)(79,1116)(80,1115)(81,1114)(82,1113)(83,1112)(84,1111)(85,1110)(86,1109)(87,1108)(88,1107)(89,1106)(90,1105)(91,1104)(92,1103)(93,1102)(94,1101)(95,1100)(96,1099)(97,1098)(98,1097)(99,1096)(100,1095)(101,1094)(102,1093)(103,1092)(104,1091)(105,1090)(106,1089)(107,1088)(108,1087)(109,1086)(110,1085)(111,1084)(112,1083)(113,1082)(114,1081)(115,1080)(116,1079)(117,1078)(118,1077)(119,1076)(120,1075)(121,1074)(122,1073)(123,1072)(124,1071)(125,1070)(126,1069)(127,1068)(128,1067)(129,1066)(130,1065)(131,1064)(132,1063)(133,1062)(134,1061)(135,1060)(136,1059)(137,1058)(138,1057)(139,1056)(140,1055)(141,1054)(142,1053)(143,1052)(144,1051)(145,1050)(146,1049)(147,1048)(148,1047)(149,1046)(150,1045)(151,1044)(152,1043)(153,1042)(154,1041)(155,1040)(156,1039)(157,1038)(158,1037)(159,1036)(160,1035)(161,1034)(162,1033)(163,1032)(164,1031)(165,1030)(166,1029)(167,1028)(168,1027)(169,1026)(170,1025)(171,1024)(172,1023)(173,1022)(174,1021)(175,1020)(176,1019)(177,1018)(178,1017)(179,1016)(180,1015)(181,1014)(182,1013)(183,1012)(184,1011)(185,1010)(186,1009)(187,1008)(188,1007)(189,1006)(190,1005)(191,1004)(192,1003)(193,1002)(194,1001)(195,1000)(196,999)(197,998)(198,997)(199,996)(200,995)(201,994)(202,993)(203,992)(204,991)(205,990)(206,989)(207,988)(208,987)(209,986)(210,985)(211,984)(212,983)(213,982)(214,981)(215,980)(216,979)(217,978)(218,977)(219,976)(220,975)(221,974)(222,973)(223,972)(224,971)(225,970)(226,969)(227,968)(228,967)(229,966)(230,965)(231,964)(232,963)(233,962)(234,961)(235,960)(236,959)(237,958)(238,957)(239,956)(240,955)(241,954)(242,953)(243,952)(244,951)(245,950)(246,949)(247,948)(248,947)(249,946)(250,945)(251,944)(252,943)(253,942)(254,941)(255,940)(256,939)(257,938)(258,937)(259,936)(260,935)(261,934)(262,933)(263,932)(264,931)(265,930)(266,929)(267,928)(268,927)(269,926)(270,925)(271,924)(272,923)(273,922)(274,921)(275,920)(276,919)(277,918)(278,917)(279,916)(280,915)(281,914)(282,913)(283,912)(284,911)(285,910)(286,909)(287,908)(288,907)(289,906)(290,905)(291,904)(292,903)(293,902)(294,901)(295,900)(296,899)(297,898)(298,897)(299,896)(300,895)(301,894)(302,893)(303,892)(304,891)(305,890)(306,889)(307,888)(308,887)(309,886)(310,885)(311,884)(312,883)(313,882)(314,881)(315,880)(316,879)(317,878)(318,877)(319,876)(320,875)(321,874)(322,873)(323,872)(324,871)(325,870)(326,869)(327,868)(328,867)(329,866)(330,865)(331,864)(332,863)(333,862)(334,861)(335,860)(336,859)(337,858)(338,857)(339,856)(340,855)(341,854)(342,853)(343,852)(344,851)(345,850)(346,849)(347,848)(348,847)(349,846)(350,845)(351,844)(352,843)(353,842)(354,841)(355,840)(356,839)(357,838)(358,837)(359,836)(360,835)(361,834)(362,833)(363,832)(364,831)(365,830)(366,829)(367,828)(368,827)(369,826)(370,825)(371,824)(372,823)(373,822)(374,821)(375,820)(376,819)(377,818)(378,817)(379,816)(380,815)(381,814)(382,813)(383,812)(384,811)(385,810)(386,809)(387,808)(388,807)(389,806)(390,805)(391,804)(392,803)(393,802)(394,801)(395,800)(396,799)(397,798)(398,797)(399,796)(400,795)(401,794)(402,793)(403,792)(404,791)(405,790)(406,789)(407,788)(408,787)(409,786)(410,785)(411,784)(412,783)(413,782)(414,781)(415,780)(416,779)(417,778)(418,777)(419,776)(420,775)(421,774)(422,773)(423,772)(424,771)(425,770)(426,769)(427,768)(428,767)(429,766)(430,765)(431,764)(432,763)(433,762)(434,761)(435,760)(436,759)(437,758)(438,757)(439,756)(440,755)(441,754)(442,753)(443,752)(444,751)(445,750)(446,749)(447,748)(448,747)(449,746)(450,745)(451,744)(452,743)(453,742)(454,741)(455,740)(456,739)(457,738)(458,737)(459,736)(460,735)(461,734)(462,733)(463,732)(464,731)(465,730)(466,729)(467,728)(468,727)(469,726)(470,725)(471,724)(472,723)(473,722)(474,721)(475,720)(476,719)(477,718)(478,717)(479,716)(480,715)(481,714)(482,713)(483,712)(484,711)(485,710)(486,709)(487,708)(488,707)(489,706)(490,705)(491,704)(492,703)(493,702)(494,701)(495,700)(496,699)(497,698)(498,697)(499,696)(500,695)(501,694)(502,693)(503,692)(504,691)(505,690)(506,689)(507,688)(508,687)(509,686)(510,685)(511,684)(512,683)(513,682)(514,681)(515,680)(516,679)(517,678)(518,677)(519,676)(520,675)(521,674)(522,673)(523,672)(524,671)(525,670)(526,669)(527,668)(528,667)(529,666)(530,665)(531,664)(532,663)(533,662)(534,661)(535,660)(536,659)(537,658)(538,657)(539,656)(540,655)(541,654)(542,653)(543,652)(544,651)(545,650)(546,649)(547,648)(548,647)(549,646)(550,645)(551,644)(552,643)(553,642)(554,641)(555,640)(556,639)(557,638)(558,637)(559,636)(560,635)(561,634)(562,633)(563,632)(564,631)(565,630)(566,629)(567,628)(568,627)(569,626)(570,625)(571,624)(572,623)(573,622)(574,621)(575,620)(576,619)(577,618)(578,617)(579,616)(580,615)(581,614)(582,613)(583,612)(584,611)(585,610)(586,609)(587,608)(588,607)(589,606)(590,605)(591,604)(592,603)(593,602)(594,601)(595,600)(596,599)(597,598)
Polycyclic presentation:
2,11,1171|b^a=b^10,c^a=c^1170
Conjugacy classes & character table
6442 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25762, 3);
Finite Group Databasebeta