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D8776 #31798150
Aliases
Splittings
Subgroups
22 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1105 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);(2,8)(3,7)(4,6)(10,1105)(11,1104)(12,1103)(13,1102)(14,1101)(15,1100)(16,1099)(17,1098)(18,1097)(19,1096)(20,1095)(21,1094)(22,1093)(23,1092)(24,1091)(25,1090)(26,1089)(27,1088)(28,1087)(29,1086)(30,1085)(31,1084)(32,1083)(33,1082)(34,1081)(35,1080)(36,1079)(37,1078)(38,1077)(39,1076)(40,1075)(41,1074)(42,1073)(43,1072)(44,1071)(45,1070)(46,1069)(47,1068)(48,1067)(49,1066)(50,1065)(51,1064)(52,1063)(53,1062)(54,1061)(55,1060)(56,1059)(57,1058)(58,1057)(59,1056)(60,1055)(61,1054)(62,1053)(63,1052)(64,1051)(65,1050)(66,1049)(67,1048)(68,1047)(69,1046)(70,1045)(71,1044)(72,1043)(73,1042)(74,1041)(75,1040)(76,1039)(77,1038)(78,1037)(79,1036)(80,1035)(81,1034)(82,1033)(83,1032)(84,1031)(85,1030)(86,1029)(87,1028)(88,1027)(89,1026)(90,1025)(91,1024)(92,1023)(93,1022)(94,1021)(95,1020)(96,1019)(97,1018)(98,1017)(99,1016)(100,1015)(101,1014)(102,1013)(103,1012)(104,1011)(105,1010)(106,1009)(107,1008)(108,1007)(109,1006)(110,1005)(111,1004)(112,1003)(113,1002)(114,1001)(115,1000)(116,999)(117,998)(118,997)(119,996)(120,995)(121,994)(122,993)(123,992)(124,991)(125,990)(126,989)(127,988)(128,987)(129,986)(130,985)(131,984)(132,983)(133,982)(134,981)(135,980)(136,979)(137,978)(138,977)(139,976)(140,975)(141,974)(142,973)(143,972)(144,971)(145,970)(146,969)(147,968)(148,967)(149,966)(150,965)(151,964)(152,963)(153,962)(154,961)(155,960)(156,959)(157,958)(158,957)(159,956)(160,955)(161,954)(162,953)(163,952)(164,951)(165,950)(166,949)(167,948)(168,947)(169,946)(170,945)(171,944)(172,943)(173,942)(174,941)(175,940)(176,939)(177,938)(178,937)(179,936)(180,935)(181,934)(182,933)(183,932)(184,931)(185,930)(186,929)(187,928)(188,927)(189,926)(190,925)(191,924)(192,923)(193,922)(194,921)(195,920)(196,919)(197,918)(198,917)(199,916)(200,915)(201,914)(202,913)(203,912)(204,911)(205,910)(206,909)(207,908)(208,907)(209,906)(210,905)(211,904)(212,903)(213,902)(214,901)(215,900)(216,899)(217,898)(218,897)(219,896)(220,895)(221,894)(222,893)(223,892)(224,891)(225,890)(226,889)(227,888)(228,887)(229,886)(230,885)(231,884)(232,883)(233,882)(234,881)(235,880)(236,879)(237,878)(238,877)(239,876)(240,875)(241,874)(242,873)(243,872)(244,871)(245,870)(246,869)(247,868)(248,867)(249,866)(250,865)(251,864)(252,863)(253,862)(254,861)(255,860)(256,859)(257,858)(258,857)(259,856)(260,855)(261,854)(262,853)(263,852)(264,851)(265,850)(266,849)(267,848)(268,847)(269,846)(270,845)(271,844)(272,843)(273,842)(274,841)(275,840)(276,839)(277,838)(278,837)(279,836)(280,835)(281,834)(282,833)(283,832)(284,831)(285,830)(286,829)(287,828)(288,827)(289,826)(290,825)(291,824)(292,823)(293,822)(294,821)(295,820)(296,819)(297,818)(298,817)(299,816)(300,815)(301,814)(302,813)(303,812)(304,811)(305,810)(306,809)(307,808)(308,807)(309,806)(310,805)(311,804)(312,803)(313,802)(314,801)(315,800)(316,799)(317,798)(318,797)(319,796)(320,795)(321,794)(322,793)(323,792)(324,791)(325,790)(326,789)(327,788)(328,787)(329,786)(330,785)(331,784)(332,783)(333,782)(334,781)(335,780)(336,779)(337,778)(338,777)(339,776)(340,775)(341,774)(342,773)(343,772)(344,771)(345,770)(346,769)(347,768)(348,767)(349,766)(350,765)(351,764)(352,763)(353,762)(354,761)(355,760)(356,759)(357,758)(358,757)(359,756)(360,755)(361,754)(362,753)(363,752)(364,751)(365,750)(366,749)(367,748)(368,747)(369,746)(370,745)(371,744)(372,743)(373,742)(374,741)(375,740)(376,739)(377,738)(378,737)(379,736)(380,735)(381,734)(382,733)(383,732)(384,731)(385,730)(386,729)(387,728)(388,727)(389,726)(390,725)(391,724)(392,723)(393,722)(394,721)(395,720)(396,719)(397,718)(398,717)(399,716)(400,715)(401,714)(402,713)(403,712)(404,711)(405,710)(406,709)(407,708)(408,707)(409,706)(410,705)(411,704)(412,703)(413,702)(414,701)(415,700)(416,699)(417,698)(418,697)(419,696)(420,695)(421,694)(422,693)(423,692)(424,691)(425,690)(426,689)(427,688)(428,687)(429,686)(430,685)(431,684)(432,683)(433,682)(434,681)(435,680)(436,679)(437,678)(438,677)(439,676)(440,675)(441,674)(442,673)(443,672)(444,671)(445,670)(446,669)(447,668)(448,667)(449,666)(450,665)(451,664)(452,663)(453,662)(454,661)(455,660)(456,659)(457,658)(458,657)(459,656)(460,655)(461,654)(462,653)(463,652)(464,651)(465,650)(466,649)(467,648)(468,647)(469,646)(470,645)(471,644)(472,643)(473,642)(474,641)(475,640)(476,639)(477,638)(478,637)(479,636)(480,635)(481,634)(482,633)(483,632)(484,631)(485,630)(486,629)(487,628)(488,627)(489,626)(490,625)(491,624)(492,623)(493,622)(494,621)(495,620)(496,619)(497,618)(498,617)(499,616)(500,615)(501,614)(502,613)(503,612)(504,611)(505,610)(506,609)(507,608)(508,607)(509,606)(510,605)(511,604)(512,603)(513,602)(514,601)(515,600)(516,599)(517,598)(518,597)(519,596)(520,595)(521,594)(522,593)(523,592)(524,591)(525,590)(526,589)(527,588)(528,587)(529,586)(530,585)(531,584)(532,583)(533,582)(534,581)(535,580)(536,579)(537,578)(538,577)(539,576)(540,575)(541,574)(542,573)(543,572)(544,571)(545,570)(546,569)(547,568)(548,567)(549,566)(550,565)(551,564)(552,563)(553,562)(554,561)(555,560)(556,559)(557,558)
Polycyclic presentation:
2^4,1097|c^2=d,b^a=bc,c^a=cd,e^a=e^1096,c^b=cd,e^b=e^1096
Conjugacy classes & character table
4391 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17552, 26);
Finite Group Databasebeta