Finite Group DatabasebetaFinite Group Databasebeta| order | 24398 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D12199 |
| unambiguous semidirect product | C11⋊D1109 |
| unambiguous semidirect product | C1109⋊D11 |
| Fitting, socle, derived, Hall | C11×C1109 ⋊ C2 |
| Sylow | C1109 ⋊ D11 |
| Sylow | C11 ⋊ D1109 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C1109 | C2 |
| LCS | G ▷ C11×C1109 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 1120 |
| transitive degree | μt(G) = 12199 |
A minimal faithful permutation representation — 2 generators on 1120 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);(2,11)(3,10)(4,9)(5,8)(6,7)(13,1120)(14,1119)(15,1118)(16,1117)(17,1116)(18,1115)(19,1114)(20,1113)(21,1112)(22,1111)(23,1110)(24,1109)(25,1108)(26,1107)(27,1106)(28,1105)(29,1104)(30,1103)(31,1102)(32,1101)(33,1100)(34,1099)(35,1098)(36,1097)(37,1096)(38,1095)(39,1094)(40,1093)(41,1092)(42,1091)(43,1090)(44,1089)(45,1088)(46,1087)(47,1086)(48,1085)(49,1084)(50,1083)(51,1082)(52,1081)(53,1080)(54,1079)(55,1078)(56,1077)(57,1076)(58,1075)(59,1074)(60,1073)(61,1072)(62,1071)(63,1070)(64,1069)(65,1068)(66,1067)(67,1066)(68,1065)(69,1064)(70,1063)(71,1062)(72,1061)(73,1060)(74,1059)(75,1058)(76,1057)(77,1056)(78,1055)(79,1054)(80,1053)(81,1052)(82,1051)(83,1050)(84,1049)(85,1048)(86,1047)(87,1046)(88,1045)(89,1044)(90,1043)(91,1042)(92,1041)(93,1040)(94,1039)(95,1038)(96,1037)(97,1036)(98,1035)(99,1034)(100,1033)(101,1032)(102,1031)(103,1030)(104,1029)(105,1028)(106,1027)(107,1026)(108,1025)(109,1024)(110,1023)(111,1022)(112,1021)(113,1020)(114,1019)(115,1018)(116,1017)(117,1016)(118,1015)(119,1014)(120,1013)(121,1012)(122,1011)(123,1010)(124,1009)(125,1008)(126,1007)(127,1006)(128,1005)(129,1004)(130,1003)(131,1002)(132,1001)(133,1000)(134,999)(135,998)(136,997)(137,996)(138,995)(139,994)(140,993)(141,992)(142,991)(143,990)(144,989)(145,988)(146,987)(147,986)(148,985)(149,984)(150,983)(151,982)(152,981)(153,980)(154,979)(155,978)(156,977)(157,976)(158,975)(159,974)(160,973)(161,972)(162,971)(163,970)(164,969)(165,968)(166,967)(167,966)(168,965)(169,964)(170,963)(171,962)(172,961)(173,960)(174,959)(175,958)(176,957)(177,956)(178,955)(179,954)(180,953)(181,952)(182,951)(183,950)(184,949)(185,948)(186,947)(187,946)(188,945)(189,944)(190,943)(191,942)(192,941)(193,940)(194,939)(195,938)(196,937)(197,936)(198,935)(199,934)(200,933)(201,932)(202,931)(203,930)(204,929)(205,928)(206,927)(207,926)(208,925)(209,924)(210,923)(211,922)(212,921)(213,920)(214,919)(215,918)(216,917)(217,916)(218,915)(219,914)(220,913)(221,912)(222,911)(223,910)(224,909)(225,908)(226,907)(227,906)(228,905)(229,904)(230,903)(231,902)(232,901)(233,900)(234,899)(235,898)(236,897)(237,896)(238,895)(239,894)(240,893)(241,892)(242,891)(243,890)(244,889)(245,888)(246,887)(247,886)(248,885)(249,884)(250,883)(251,882)(252,881)(253,880)(254,879)(255,878)(256,877)(257,876)(258,875)(259,874)(260,873)(261,872)(262,871)(263,870)(264,869)(265,868)(266,867)(267,866)(268,865)(269,864)(270,863)(271,862)(272,861)(273,860)(274,859)(275,858)(276,857)(277,856)(278,855)(279,854)(280,853)(281,852)(282,851)(283,850)(284,849)(285,848)(286,847)(287,846)(288,845)(289,844)(290,843)(291,842)(292,841)(293,840)(294,839)(295,838)(296,837)(297,836)(298,835)(299,834)(300,833)(301,832)(302,831)(303,830)(304,829)(305,828)(306,827)(307,826)(308,825)(309,824)(310,823)(311,822)(312,821)(313,820)(314,819)(315,818)(316,817)(317,816)(318,815)(319,814)(320,813)(321,812)(322,811)(323,810)(324,809)(325,808)(326,807)(327,806)(328,805)(329,804)(330,803)(331,802)(332,801)(333,800)(334,799)(335,798)(336,797)(337,796)(338,795)(339,794)(340,793)(341,792)(342,791)(343,790)(344,789)(345,788)(346,787)(347,786)(348,785)(349,784)(350,783)(351,782)(352,781)(353,780)(354,779)(355,778)(356,777)(357,776)(358,775)(359,774)(360,773)(361,772)(362,771)(363,770)(364,769)(365,768)(366,767)(367,766)(368,765)(369,764)(370,763)(371,762)(372,761)(373,760)(374,759)(375,758)(376,757)(377,756)(378,755)(379,754)(380,753)(381,752)(382,751)(383,750)(384,749)(385,748)(386,747)(387,746)(388,745)(389,744)(390,743)(391,742)(392,741)(393,740)(394,739)(395,738)(396,737)(397,736)(398,735)(399,734)(400,733)(401,732)(402,731)(403,730)(404,729)(405,728)(406,727)(407,726)(408,725)(409,724)(410,723)(411,722)(412,721)(413,720)(414,719)(415,718)(416,717)(417,716)(418,715)(419,714)(420,713)(421,712)(422,711)(423,710)(424,709)(425,708)(426,707)(427,706)(428,705)(429,704)(430,703)(431,702)(432,701)(433,700)(434,699)(435,698)(436,697)(437,696)(438,695)(439,694)(440,693)(441,692)(442,691)(443,690)(444,689)(445,688)(446,687)(447,686)(448,685)(449,684)(450,683)(451,682)(452,681)(453,680)(454,679)(455,678)(456,677)(457,676)(458,675)(459,674)(460,673)(461,672)(462,671)(463,670)(464,669)(465,668)(466,667)(467,666)(468,665)(469,664)(470,663)(471,662)(472,661)(473,660)(474,659)(475,658)(476,657)(477,656)(478,655)(479,654)(480,653)(481,652)(482,651)(483,650)(484,649)(485,648)(486,647)(487,646)(488,645)(489,644)(490,643)(491,642)(492,641)(493,640)(494,639)(495,638)(496,637)(497,636)(498,635)(499,634)(500,633)(501,632)(502,631)(503,630)(504,629)(505,628)(506,627)(507,626)(508,625)(509,624)(510,623)(511,622)(512,621)(513,620)(514,619)(515,618)(516,617)(517,616)(518,615)(519,614)(520,613)(521,612)(522,611)(523,610)(524,609)(525,608)(526,607)(527,606)(528,605)(529,604)(530,603)(531,602)(532,601)(533,600)(534,599)(535,598)(536,597)(537,596)(538,595)(539,594)(540,593)(541,592)(542,591)(543,590)(544,589)(545,588)(546,587)(547,586)(548,585)(549,584)(550,583)(551,582)(552,581)(553,580)(554,579)(555,578)(556,577)(557,576)(558,575)(559,574)(560,573)(561,572)(562,571)(563,570)(564,569)(565,568)(566,567)Polycyclic presentation:
2,11,1109|b^a=b^10,c^a=c^11086101 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24398, 3);