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Dic5755 #37527700
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1160 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);(1,3,2,4)(6,9)(7,8)(11,1160)(12,1159)(13,1158)(14,1157)(15,1156)(16,1155)(17,1154)(18,1153)(19,1152)(20,1151)(21,1150)(22,1149)(23,1148)(24,1147)(25,1146)(26,1145)(27,1144)(28,1143)(29,1142)(30,1141)(31,1140)(32,1139)(33,1138)(34,1137)(35,1136)(36,1135)(37,1134)(38,1133)(39,1132)(40,1131)(41,1130)(42,1129)(43,1128)(44,1127)(45,1126)(46,1125)(47,1124)(48,1123)(49,1122)(50,1121)(51,1120)(52,1119)(53,1118)(54,1117)(55,1116)(56,1115)(57,1114)(58,1113)(59,1112)(60,1111)(61,1110)(62,1109)(63,1108)(64,1107)(65,1106)(66,1105)(67,1104)(68,1103)(69,1102)(70,1101)(71,1100)(72,1099)(73,1098)(74,1097)(75,1096)(76,1095)(77,1094)(78,1093)(79,1092)(80,1091)(81,1090)(82,1089)(83,1088)(84,1087)(85,1086)(86,1085)(87,1084)(88,1083)(89,1082)(90,1081)(91,1080)(92,1079)(93,1078)(94,1077)(95,1076)(96,1075)(97,1074)(98,1073)(99,1072)(100,1071)(101,1070)(102,1069)(103,1068)(104,1067)(105,1066)(106,1065)(107,1064)(108,1063)(109,1062)(110,1061)(111,1060)(112,1059)(113,1058)(114,1057)(115,1056)(116,1055)(117,1054)(118,1053)(119,1052)(120,1051)(121,1050)(122,1049)(123,1048)(124,1047)(125,1046)(126,1045)(127,1044)(128,1043)(129,1042)(130,1041)(131,1040)(132,1039)(133,1038)(134,1037)(135,1036)(136,1035)(137,1034)(138,1033)(139,1032)(140,1031)(141,1030)(142,1029)(143,1028)(144,1027)(145,1026)(146,1025)(147,1024)(148,1023)(149,1022)(150,1021)(151,1020)(152,1019)(153,1018)(154,1017)(155,1016)(156,1015)(157,1014)(158,1013)(159,1012)(160,1011)(161,1010)(162,1009)(163,1008)(164,1007)(165,1006)(166,1005)(167,1004)(168,1003)(169,1002)(170,1001)(171,1000)(172,999)(173,998)(174,997)(175,996)(176,995)(177,994)(178,993)(179,992)(180,991)(181,990)(182,989)(183,988)(184,987)(185,986)(186,985)(187,984)(188,983)(189,982)(190,981)(191,980)(192,979)(193,978)(194,977)(195,976)(196,975)(197,974)(198,973)(199,972)(200,971)(201,970)(202,969)(203,968)(204,967)(205,966)(206,965)(207,964)(208,963)(209,962)(210,961)(211,960)(212,959)(213,958)(214,957)(215,956)(216,955)(217,954)(218,953)(219,952)(220,951)(221,950)(222,949)(223,948)(224,947)(225,946)(226,945)(227,944)(228,943)(229,942)(230,941)(231,940)(232,939)(233,938)(234,937)(235,936)(236,935)(237,934)(238,933)(239,932)(240,931)(241,930)(242,929)(243,928)(244,927)(245,926)(246,925)(247,924)(248,923)(249,922)(250,921)(251,920)(252,919)(253,918)(254,917)(255,916)(256,915)(257,914)(258,913)(259,912)(260,911)(261,910)(262,909)(263,908)(264,907)(265,906)(266,905)(267,904)(268,903)(269,902)(270,901)(271,900)(272,899)(273,898)(274,897)(275,896)(276,895)(277,894)(278,893)(279,892)(280,891)(281,890)(282,889)(283,888)(284,887)(285,886)(286,885)(287,884)(288,883)(289,882)(290,881)(291,880)(292,879)(293,878)(294,877)(295,876)(296,875)(297,874)(298,873)(299,872)(300,871)(301,870)(302,869)(303,868)(304,867)(305,866)(306,865)(307,864)(308,863)(309,862)(310,861)(311,860)(312,859)(313,858)(314,857)(315,856)(316,855)(317,854)(318,853)(319,852)(320,851)(321,850)(322,849)(323,848)(324,847)(325,846)(326,845)(327,844)(328,843)(329,842)(330,841)(331,840)(332,839)(333,838)(334,837)(335,836)(336,835)(337,834)(338,833)(339,832)(340,831)(341,830)(342,829)(343,828)(344,827)(345,826)(346,825)(347,824)(348,823)(349,822)(350,821)(351,820)(352,819)(353,818)(354,817)(355,816)(356,815)(357,814)(358,813)(359,812)(360,811)(361,810)(362,809)(363,808)(364,807)(365,806)(366,805)(367,804)(368,803)(369,802)(370,801)(371,800)(372,799)(373,798)(374,797)(375,796)(376,795)(377,794)(378,793)(379,792)(380,791)(381,790)(382,789)(383,788)(384,787)(385,786)(386,785)(387,784)(388,783)(389,782)(390,781)(391,780)(392,779)(393,778)(394,777)(395,776)(396,775)(397,774)(398,773)(399,772)(400,771)(401,770)(402,769)(403,768)(404,767)(405,766)(406,765)(407,764)(408,763)(409,762)(410,761)(411,760)(412,759)(413,758)(414,757)(415,756)(416,755)(417,754)(418,753)(419,752)(420,751)(421,750)(422,749)(423,748)(424,747)(425,746)(426,745)(427,744)(428,743)(429,742)(430,741)(431,740)(432,739)(433,738)(434,737)(435,736)(436,735)(437,734)(438,733)(439,732)(440,731)(441,730)(442,729)(443,728)(444,727)(445,726)(446,725)(447,724)(448,723)(449,722)(450,721)(451,720)(452,719)(453,718)(454,717)(455,716)(456,715)(457,714)(458,713)(459,712)(460,711)(461,710)(462,709)(463,708)(464,707)(465,706)(466,705)(467,704)(468,703)(469,702)(470,701)(471,700)(472,699)(473,698)(474,697)(475,696)(476,695)(477,694)(478,693)(479,692)(480,691)(481,690)(482,689)(483,688)(484,687)(485,686)(486,685)(487,684)(488,683)(489,682)(490,681)(491,680)(492,679)(493,678)(494,677)(495,676)(496,675)(497,674)(498,673)(499,672)(500,671)(501,670)(502,669)(503,668)(504,667)(505,666)(506,665)(507,664)(508,663)(509,662)(510,661)(511,660)(512,659)(513,658)(514,657)(515,656)(516,655)(517,654)(518,653)(519,652)(520,651)(521,650)(522,649)(523,648)(524,647)(525,646)(526,645)(527,644)(528,643)(529,642)(530,641)(531,640)(532,639)(533,638)(534,637)(535,636)(536,635)(537,634)(538,633)(539,632)(540,631)(541,630)(542,629)(543,628)(544,627)(545,626)(546,625)(547,624)(548,623)(549,622)(550,621)(551,620)(552,619)(553,618)(554,617)(555,616)(556,615)(557,614)(558,613)(559,612)(560,611)(561,610)(562,609)(563,608)(564,607)(565,606)(566,605)(567,604)(568,603)(569,602)(570,601)(571,600)(572,599)(573,598)(574,597)(575,596)(576,595)(577,594)(578,593)(579,592)(580,591)(581,590)(582,589)(583,588)(584,587)(585,586)
Polycyclic presentation:
2,5,1151,2|a^2=d,b^a=b^4,c^a=c^1150
Conjugacy classes & character table
5758 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23020, 6);
Finite Group Databasebeta