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