← Prev (#47975701) Next (#47975703) →
Aliases
Splittings
Subgroups
16 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1179 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);(5,8)(6,7)(10,1179)(11,1178)(12,1177)(13,1176)(14,1175)(15,1174)(16,1173)(17,1172)(18,1171)(19,1170)(20,1169)(21,1168)(22,1167)(23,1166)(24,1165)(25,1164)(26,1163)(27,1162)(28,1161)(29,1160)(30,1159)(31,1158)(32,1157)(33,1156)(34,1155)(35,1154)(36,1153)(37,1152)(38,1151)(39,1150)(40,1149)(41,1148)(42,1147)(43,1146)(44,1145)(45,1144)(46,1143)(47,1142)(48,1141)(49,1140)(50,1139)(51,1138)(52,1137)(53,1136)(54,1135)(55,1134)(56,1133)(57,1132)(58,1131)(59,1130)(60,1129)(61,1128)(62,1127)(63,1126)(64,1125)(65,1124)(66,1123)(67,1122)(68,1121)(69,1120)(70,1119)(71,1118)(72,1117)(73,1116)(74,1115)(75,1114)(76,1113)(77,1112)(78,1111)(79,1110)(80,1109)(81,1108)(82,1107)(83,1106)(84,1105)(85,1104)(86,1103)(87,1102)(88,1101)(89,1100)(90,1099)(91,1098)(92,1097)(93,1096)(94,1095)(95,1094)(96,1093)(97,1092)(98,1091)(99,1090)(100,1089)(101,1088)(102,1087)(103,1086)(104,1085)(105,1084)(106,1083)(107,1082)(108,1081)(109,1080)(110,1079)(111,1078)(112,1077)(113,1076)(114,1075)(115,1074)(116,1073)(117,1072)(118,1071)(119,1070)(120,1069)(121,1068)(122,1067)(123,1066)(124,1065)(125,1064)(126,1063)(127,1062)(128,1061)(129,1060)(130,1059)(131,1058)(132,1057)(133,1056)(134,1055)(135,1054)(136,1053)(137,1052)(138,1051)(139,1050)(140,1049)(141,1048)(142,1047)(143,1046)(144,1045)(145,1044)(146,1043)(147,1042)(148,1041)(149,1040)(150,1039)(151,1038)(152,1037)(153,1036)(154,1035)(155,1034)(156,1033)(157,1032)(158,1031)(159,1030)(160,1029)(161,1028)(162,1027)(163,1026)(164,1025)(165,1024)(166,1023)(167,1022)(168,1021)(169,1020)(170,1019)(171,1018)(172,1017)(173,1016)(174,1015)(175,1014)(176,1013)(177,1012)(178,1011)(179,1010)(180,1009)(181,1008)(182,1007)(183,1006)(184,1005)(185,1004)(186,1003)(187,1002)(188,1001)(189,1000)(190,999)(191,998)(192,997)(193,996)(194,995)(195,994)(196,993)(197,992)(198,991)(199,990)(200,989)(201,988)(202,987)(203,986)(204,985)(205,984)(206,983)(207,982)(208,981)(209,980)(210,979)(211,978)(212,977)(213,976)(214,975)(215,974)(216,973)(217,972)(218,971)(219,970)(220,969)(221,968)(222,967)(223,966)(224,965)(225,964)(226,963)(227,962)(228,961)(229,960)(230,959)(231,958)(232,957)(233,956)(234,955)(235,954)(236,953)(237,952)(238,951)(239,950)(240,949)(241,948)(242,947)(243,946)(244,945)(245,944)(246,943)(247,942)(248,941)(249,940)(250,939)(251,938)(252,937)(253,936)(254,935)(255,934)(256,933)(257,932)(258,931)(259,930)(260,929)(261,928)(262,927)(263,926)(264,925)(265,924)(266,923)(267,922)(268,921)(269,920)(270,919)(271,918)(272,917)(273,916)(274,915)(275,914)(276,913)(277,912)(278,911)(279,910)(280,909)(281,908)(282,907)(283,906)(284,905)(285,904)(286,903)(287,902)(288,901)(289,900)(290,899)(291,898)(292,897)(293,896)(294,895)(295,894)(296,893)(297,892)(298,891)(299,890)(300,889)(301,888)(302,887)(303,886)(304,885)(305,884)(306,883)(307,882)(308,881)(309,880)(310,879)(311,878)(312,877)(313,876)(314,875)(315,874)(316,873)(317,872)(318,871)(319,870)(320,869)(321,868)(322,867)(323,866)(324,865)(325,864)(326,863)(327,862)(328,861)(329,860)(330,859)(331,858)(332,857)(333,856)(334,855)(335,854)(336,853)(337,852)(338,851)(339,850)(340,849)(341,848)(342,847)(343,846)(344,845)(345,844)(346,843)(347,842)(348,841)(349,840)(350,839)(351,838)(352,837)(353,836)(354,835)(355,834)(356,833)(357,832)(358,831)(359,830)(360,829)(361,828)(362,827)(363,826)(364,825)(365,824)(366,823)(367,822)(368,821)(369,820)(370,819)(371,818)(372,817)(373,816)(374,815)(375,814)(376,813)(377,812)(378,811)(379,810)(380,809)(381,808)(382,807)(383,806)(384,805)(385,804)(386,803)(387,802)(388,801)(389,800)(390,799)(391,798)(392,797)(393,796)(394,795)(395,794)(396,793)(397,792)(398,791)(399,790)(400,789)(401,788)(402,787)(403,786)(404,785)(405,784)(406,783)(407,782)(408,781)(409,780)(410,779)(411,778)(412,777)(413,776)(414,775)(415,774)(416,773)(417,772)(418,771)(419,770)(420,769)(421,768)(422,767)(423,766)(424,765)(425,764)(426,763)(427,762)(428,761)(429,760)(430,759)(431,758)(432,757)(433,756)(434,755)(435,754)(436,753)(437,752)(438,751)(439,750)(440,749)(441,748)(442,747)(443,746)(444,745)(445,744)(446,743)(447,742)(448,741)(449,740)(450,739)(451,738)(452,737)(453,736)(454,735)(455,734)(456,733)(457,732)(458,731)(459,730)(460,729)(461,728)(462,727)(463,726)(464,725)(465,724)(466,723)(467,722)(468,721)(469,720)(470,719)(471,718)(472,717)(473,716)(474,715)(475,714)(476,713)(477,712)(478,711)(479,710)(480,709)(481,708)(482,707)(483,706)(484,705)(485,704)(486,703)(487,702)(488,701)(489,700)(490,699)(491,698)(492,697)(493,696)(494,695)(495,694)(496,693)(497,692)(498,691)(499,690)(500,689)(501,688)(502,687)(503,686)(504,685)(505,684)(506,683)(507,682)(508,681)(509,680)(510,679)(511,678)(512,677)(513,676)(514,675)(515,674)(516,673)(517,672)(518,671)(519,670)(520,669)(521,668)(522,667)(523,666)(524,665)(525,664)(526,663)(527,662)(528,661)(529,660)(530,659)(531,658)(532,657)(533,656)(534,655)(535,654)(536,653)(537,652)(538,651)(539,650)(540,649)(541,648)(542,647)(543,646)(544,645)(545,644)(546,643)(547,642)(548,641)(549,640)(550,639)(551,638)(552,637)(553,636)(554,635)(555,634)(556,633)(557,632)(558,631)(559,630)(560,629)(561,628)(562,627)(563,626)(564,625)(565,624)(566,623)(567,622)(568,621)(569,620)(570,619)(571,618)(572,617)(573,616)(574,615)(575,614)(576,613)(577,612)(578,611)(579,610)(580,609)(581,608)(582,607)(583,606)(584,605)(585,604)(586,603)(587,602)(588,601)(589,600)(590,599)(591,598)(592,597)(593,596)(594,595)
Conjugacy classes & character table
8787 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35130, 7);
Finite Group Databasebeta