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D8936 #31821896
Aliases
Splittings
Subgroups
22 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1125 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);(2,8)(3,7)(4,6)(10,1125)(11,1124)(12,1123)(13,1122)(14,1121)(15,1120)(16,1119)(17,1118)(18,1117)(19,1116)(20,1115)(21,1114)(22,1113)(23,1112)(24,1111)(25,1110)(26,1109)(27,1108)(28,1107)(29,1106)(30,1105)(31,1104)(32,1103)(33,1102)(34,1101)(35,1100)(36,1099)(37,1098)(38,1097)(39,1096)(40,1095)(41,1094)(42,1093)(43,1092)(44,1091)(45,1090)(46,1089)(47,1088)(48,1087)(49,1086)(50,1085)(51,1084)(52,1083)(53,1082)(54,1081)(55,1080)(56,1079)(57,1078)(58,1077)(59,1076)(60,1075)(61,1074)(62,1073)(63,1072)(64,1071)(65,1070)(66,1069)(67,1068)(68,1067)(69,1066)(70,1065)(71,1064)(72,1063)(73,1062)(74,1061)(75,1060)(76,1059)(77,1058)(78,1057)(79,1056)(80,1055)(81,1054)(82,1053)(83,1052)(84,1051)(85,1050)(86,1049)(87,1048)(88,1047)(89,1046)(90,1045)(91,1044)(92,1043)(93,1042)(94,1041)(95,1040)(96,1039)(97,1038)(98,1037)(99,1036)(100,1035)(101,1034)(102,1033)(103,1032)(104,1031)(105,1030)(106,1029)(107,1028)(108,1027)(109,1026)(110,1025)(111,1024)(112,1023)(113,1022)(114,1021)(115,1020)(116,1019)(117,1018)(118,1017)(119,1016)(120,1015)(121,1014)(122,1013)(123,1012)(124,1011)(125,1010)(126,1009)(127,1008)(128,1007)(129,1006)(130,1005)(131,1004)(132,1003)(133,1002)(134,1001)(135,1000)(136,999)(137,998)(138,997)(139,996)(140,995)(141,994)(142,993)(143,992)(144,991)(145,990)(146,989)(147,988)(148,987)(149,986)(150,985)(151,984)(152,983)(153,982)(154,981)(155,980)(156,979)(157,978)(158,977)(159,976)(160,975)(161,974)(162,973)(163,972)(164,971)(165,970)(166,969)(167,968)(168,967)(169,966)(170,965)(171,964)(172,963)(173,962)(174,961)(175,960)(176,959)(177,958)(178,957)(179,956)(180,955)(181,954)(182,953)(183,952)(184,951)(185,950)(186,949)(187,948)(188,947)(189,946)(190,945)(191,944)(192,943)(193,942)(194,941)(195,940)(196,939)(197,938)(198,937)(199,936)(200,935)(201,934)(202,933)(203,932)(204,931)(205,930)(206,929)(207,928)(208,927)(209,926)(210,925)(211,924)(212,923)(213,922)(214,921)(215,920)(216,919)(217,918)(218,917)(219,916)(220,915)(221,914)(222,913)(223,912)(224,911)(225,910)(226,909)(227,908)(228,907)(229,906)(230,905)(231,904)(232,903)(233,902)(234,901)(235,900)(236,899)(237,898)(238,897)(239,896)(240,895)(241,894)(242,893)(243,892)(244,891)(245,890)(246,889)(247,888)(248,887)(249,886)(250,885)(251,884)(252,883)(253,882)(254,881)(255,880)(256,879)(257,878)(258,877)(259,876)(260,875)(261,874)(262,873)(263,872)(264,871)(265,870)(266,869)(267,868)(268,867)(269,866)(270,865)(271,864)(272,863)(273,862)(274,861)(275,860)(276,859)(277,858)(278,857)(279,856)(280,855)(281,854)(282,853)(283,852)(284,851)(285,850)(286,849)(287,848)(288,847)(289,846)(290,845)(291,844)(292,843)(293,842)(294,841)(295,840)(296,839)(297,838)(298,837)(299,836)(300,835)(301,834)(302,833)(303,832)(304,831)(305,830)(306,829)(307,828)(308,827)(309,826)(310,825)(311,824)(312,823)(313,822)(314,821)(315,820)(316,819)(317,818)(318,817)(319,816)(320,815)(321,814)(322,813)(323,812)(324,811)(325,810)(326,809)(327,808)(328,807)(329,806)(330,805)(331,804)(332,803)(333,802)(334,801)(335,800)(336,799)(337,798)(338,797)(339,796)(340,795)(341,794)(342,793)(343,792)(344,791)(345,790)(346,789)(347,788)(348,787)(349,786)(350,785)(351,784)(352,783)(353,782)(354,781)(355,780)(356,779)(357,778)(358,777)(359,776)(360,775)(361,774)(362,773)(363,772)(364,771)(365,770)(366,769)(367,768)(368,767)(369,766)(370,765)(371,764)(372,763)(373,762)(374,761)(375,760)(376,759)(377,758)(378,757)(379,756)(380,755)(381,754)(382,753)(383,752)(384,751)(385,750)(386,749)(387,748)(388,747)(389,746)(390,745)(391,744)(392,743)(393,742)(394,741)(395,740)(396,739)(397,738)(398,737)(399,736)(400,735)(401,734)(402,733)(403,732)(404,731)(405,730)(406,729)(407,728)(408,727)(409,726)(410,725)(411,724)(412,723)(413,722)(414,721)(415,720)(416,719)(417,718)(418,717)(419,716)(420,715)(421,714)(422,713)(423,712)(424,711)(425,710)(426,709)(427,708)(428,707)(429,706)(430,705)(431,704)(432,703)(433,702)(434,701)(435,700)(436,699)(437,698)(438,697)(439,696)(440,695)(441,694)(442,693)(443,692)(444,691)(445,690)(446,689)(447,688)(448,687)(449,686)(450,685)(451,684)(452,683)(453,682)(454,681)(455,680)(456,679)(457,678)(458,677)(459,676)(460,675)(461,674)(462,673)(463,672)(464,671)(465,670)(466,669)(467,668)(468,667)(469,666)(470,665)(471,664)(472,663)(473,662)(474,661)(475,660)(476,659)(477,658)(478,657)(479,656)(480,655)(481,654)(482,653)(483,652)(484,651)(485,650)(486,649)(487,648)(488,647)(489,646)(490,645)(491,644)(492,643)(493,642)(494,641)(495,640)(496,639)(497,638)(498,637)(499,636)(500,635)(501,634)(502,633)(503,632)(504,631)(505,630)(506,629)(507,628)(508,627)(509,626)(510,625)(511,624)(512,623)(513,622)(514,621)(515,620)(516,619)(517,618)(518,617)(519,616)(520,615)(521,614)(522,613)(523,612)(524,611)(525,610)(526,609)(527,608)(528,607)(529,606)(530,605)(531,604)(532,603)(533,602)(534,601)(535,600)(536,599)(537,598)(538,597)(539,596)(540,595)(541,594)(542,593)(543,592)(544,591)(545,590)(546,589)(547,588)(548,587)(549,586)(550,585)(551,584)(552,583)(553,582)(554,581)(555,580)(556,579)(557,578)(558,577)(559,576)(560,575)(561,574)(562,573)(563,572)(564,571)(565,570)(566,569)(567,568)
Polycyclic presentation:
2^4,1117|c^2=d,b^a=bc,c^a=cd,e^a=e^1116,c^b=cd,e^b=e^1116
Conjugacy classes & character table
4471 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17872, 26);
Finite Group Databasebeta