Finite Group DatabasebetaFinite Group Databasebeta| order | 24706 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D12353 |
| unambiguous semidirect product | C11⋊D1123 |
| unambiguous semidirect product | C1123⋊D11 |
| Fitting, socle, derived, Hall | C11×C1123 ⋊ C2 |
| Sylow | C1123 ⋊ D11 |
| Sylow | C11 ⋊ D1123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C1123 | C2 |
| LCS | G ▷ C11×C1123 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 1134 |
| transitive degree | μt(G) = 12353 |
A minimal faithful permutation representation — 2 generators on 1134 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);(2,11)(3,10)(4,9)(5,8)(6,7)(13,1134)(14,1133)(15,1132)(16,1131)(17,1130)(18,1129)(19,1128)(20,1127)(21,1126)(22,1125)(23,1124)(24,1123)(25,1122)(26,1121)(27,1120)(28,1119)(29,1118)(30,1117)(31,1116)(32,1115)(33,1114)(34,1113)(35,1112)(36,1111)(37,1110)(38,1109)(39,1108)(40,1107)(41,1106)(42,1105)(43,1104)(44,1103)(45,1102)(46,1101)(47,1100)(48,1099)(49,1098)(50,1097)(51,1096)(52,1095)(53,1094)(54,1093)(55,1092)(56,1091)(57,1090)(58,1089)(59,1088)(60,1087)(61,1086)(62,1085)(63,1084)(64,1083)(65,1082)(66,1081)(67,1080)(68,1079)(69,1078)(70,1077)(71,1076)(72,1075)(73,1074)(74,1073)(75,1072)(76,1071)(77,1070)(78,1069)(79,1068)(80,1067)(81,1066)(82,1065)(83,1064)(84,1063)(85,1062)(86,1061)(87,1060)(88,1059)(89,1058)(90,1057)(91,1056)(92,1055)(93,1054)(94,1053)(95,1052)(96,1051)(97,1050)(98,1049)(99,1048)(100,1047)(101,1046)(102,1045)(103,1044)(104,1043)(105,1042)(106,1041)(107,1040)(108,1039)(109,1038)(110,1037)(111,1036)(112,1035)(113,1034)(114,1033)(115,1032)(116,1031)(117,1030)(118,1029)(119,1028)(120,1027)(121,1026)(122,1025)(123,1024)(124,1023)(125,1022)(126,1021)(127,1020)(128,1019)(129,1018)(130,1017)(131,1016)(132,1015)(133,1014)(134,1013)(135,1012)(136,1011)(137,1010)(138,1009)(139,1008)(140,1007)(141,1006)(142,1005)(143,1004)(144,1003)(145,1002)(146,1001)(147,1000)(148,999)(149,998)(150,997)(151,996)(152,995)(153,994)(154,993)(155,992)(156,991)(157,990)(158,989)(159,988)(160,987)(161,986)(162,985)(163,984)(164,983)(165,982)(166,981)(167,980)(168,979)(169,978)(170,977)(171,976)(172,975)(173,974)(174,973)(175,972)(176,971)(177,970)(178,969)(179,968)(180,967)(181,966)(182,965)(183,964)(184,963)(185,962)(186,961)(187,960)(188,959)(189,958)(190,957)(191,956)(192,955)(193,954)(194,953)(195,952)(196,951)(197,950)(198,949)(199,948)(200,947)(201,946)(202,945)(203,944)(204,943)(205,942)(206,941)(207,940)(208,939)(209,938)(210,937)(211,936)(212,935)(213,934)(214,933)(215,932)(216,931)(217,930)(218,929)(219,928)(220,927)(221,926)(222,925)(223,924)(224,923)(225,922)(226,921)(227,920)(228,919)(229,918)(230,917)(231,916)(232,915)(233,914)(234,913)(235,912)(236,911)(237,910)(238,909)(239,908)(240,907)(241,906)(242,905)(243,904)(244,903)(245,902)(246,901)(247,900)(248,899)(249,898)(250,897)(251,896)(252,895)(253,894)(254,893)(255,892)(256,891)(257,890)(258,889)(259,888)(260,887)(261,886)(262,885)(263,884)(264,883)(265,882)(266,881)(267,880)(268,879)(269,878)(270,877)(271,876)(272,875)(273,874)(274,873)(275,872)(276,871)(277,870)(278,869)(279,868)(280,867)(281,866)(282,865)(283,864)(284,863)(285,862)(286,861)(287,860)(288,859)(289,858)(290,857)(291,856)(292,855)(293,854)(294,853)(295,852)(296,851)(297,850)(298,849)(299,848)(300,847)(301,846)(302,845)(303,844)(304,843)(305,842)(306,841)(307,840)(308,839)(309,838)(310,837)(311,836)(312,835)(313,834)(314,833)(315,832)(316,831)(317,830)(318,829)(319,828)(320,827)(321,826)(322,825)(323,824)(324,823)(325,822)(326,821)(327,820)(328,819)(329,818)(330,817)(331,816)(332,815)(333,814)(334,813)(335,812)(336,811)(337,810)(338,809)(339,808)(340,807)(341,806)(342,805)(343,804)(344,803)(345,802)(346,801)(347,800)(348,799)(349,798)(350,797)(351,796)(352,795)(353,794)(354,793)(355,792)(356,791)(357,790)(358,789)(359,788)(360,787)(361,786)(362,785)(363,784)(364,783)(365,782)(366,781)(367,780)(368,779)(369,778)(370,777)(371,776)(372,775)(373,774)(374,773)(375,772)(376,771)(377,770)(378,769)(379,768)(380,767)(381,766)(382,765)(383,764)(384,763)(385,762)(386,761)(387,760)(388,759)(389,758)(390,757)(391,756)(392,755)(393,754)(394,753)(395,752)(396,751)(397,750)(398,749)(399,748)(400,747)(401,746)(402,745)(403,744)(404,743)(405,742)(406,741)(407,740)(408,739)(409,738)(410,737)(411,736)(412,735)(413,734)(414,733)(415,732)(416,731)(417,730)(418,729)(419,728)(420,727)(421,726)(422,725)(423,724)(424,723)(425,722)(426,721)(427,720)(428,719)(429,718)(430,717)(431,716)(432,715)(433,714)(434,713)(435,712)(436,711)(437,710)(438,709)(439,708)(440,707)(441,706)(442,705)(443,704)(444,703)(445,702)(446,701)(447,700)(448,699)(449,698)(450,697)(451,696)(452,695)(453,694)(454,693)(455,692)(456,691)(457,690)(458,689)(459,688)(460,687)(461,686)(462,685)(463,684)(464,683)(465,682)(466,681)(467,680)(468,679)(469,678)(470,677)(471,676)(472,675)(473,674)(474,673)(475,672)(476,671)(477,670)(478,669)(479,668)(480,667)(481,666)(482,665)(483,664)(484,663)(485,662)(486,661)(487,660)(488,659)(489,658)(490,657)(491,656)(492,655)(493,654)(494,653)(495,652)(496,651)(497,650)(498,649)(499,648)(500,647)(501,646)(502,645)(503,644)(504,643)(505,642)(506,641)(507,640)(508,639)(509,638)(510,637)(511,636)(512,635)(513,634)(514,633)(515,632)(516,631)(517,630)(518,629)(519,628)(520,627)(521,626)(522,625)(523,624)(524,623)(525,622)(526,621)(527,620)(528,619)(529,618)(530,617)(531,616)(532,615)(533,614)(534,613)(535,612)(536,611)(537,610)(538,609)(539,608)(540,607)(541,606)(542,605)(543,604)(544,603)(545,602)(546,601)(547,600)(548,599)(549,598)(550,597)(551,596)(552,595)(553,594)(554,593)(555,592)(556,591)(557,590)(558,589)(559,588)(560,587)(561,586)(562,585)(563,584)(564,583)(565,582)(566,581)(567,580)(568,579)(569,578)(570,577)(571,576)(572,575)(573,574)Polycyclic presentation:
2,11,1123|b^a=b^10,c^a=c^11226178 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24706, 5);