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D9448 #34038577
Aliases
Splittings
Subgroups
22 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1189 points:
(1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189);(2,8)(3,7)(4,6)(10,1189)(11,1188)(12,1187)(13,1186)(14,1185)(15,1184)(16,1183)(17,1182)(18,1181)(19,1180)(20,1179)(21,1178)(22,1177)(23,1176)(24,1175)(25,1174)(26,1173)(27,1172)(28,1171)(29,1170)(30,1169)(31,1168)(32,1167)(33,1166)(34,1165)(35,1164)(36,1163)(37,1162)(38,1161)(39,1160)(40,1159)(41,1158)(42,1157)(43,1156)(44,1155)(45,1154)(46,1153)(47,1152)(48,1151)(49,1150)(50,1149)(51,1148)(52,1147)(53,1146)(54,1145)(55,1144)(56,1143)(57,1142)(58,1141)(59,1140)(60,1139)(61,1138)(62,1137)(63,1136)(64,1135)(65,1134)(66,1133)(67,1132)(68,1131)(69,1130)(70,1129)(71,1128)(72,1127)(73,1126)(74,1125)(75,1124)(76,1123)(77,1122)(78,1121)(79,1120)(80,1119)(81,1118)(82,1117)(83,1116)(84,1115)(85,1114)(86,1113)(87,1112)(88,1111)(89,1110)(90,1109)(91,1108)(92,1107)(93,1106)(94,1105)(95,1104)(96,1103)(97,1102)(98,1101)(99,1100)(100,1099)(101,1098)(102,1097)(103,1096)(104,1095)(105,1094)(106,1093)(107,1092)(108,1091)(109,1090)(110,1089)(111,1088)(112,1087)(113,1086)(114,1085)(115,1084)(116,1083)(117,1082)(118,1081)(119,1080)(120,1079)(121,1078)(122,1077)(123,1076)(124,1075)(125,1074)(126,1073)(127,1072)(128,1071)(129,1070)(130,1069)(131,1068)(132,1067)(133,1066)(134,1065)(135,1064)(136,1063)(137,1062)(138,1061)(139,1060)(140,1059)(141,1058)(142,1057)(143,1056)(144,1055)(145,1054)(146,1053)(147,1052)(148,1051)(149,1050)(150,1049)(151,1048)(152,1047)(153,1046)(154,1045)(155,1044)(156,1043)(157,1042)(158,1041)(159,1040)(160,1039)(161,1038)(162,1037)(163,1036)(164,1035)(165,1034)(166,1033)(167,1032)(168,1031)(169,1030)(170,1029)(171,1028)(172,1027)(173,1026)(174,1025)(175,1024)(176,1023)(177,1022)(178,1021)(179,1020)(180,1019)(181,1018)(182,1017)(183,1016)(184,1015)(185,1014)(186,1013)(187,1012)(188,1011)(189,1010)(190,1009)(191,1008)(192,1007)(193,1006)(194,1005)(195,1004)(196,1003)(197,1002)(198,1001)(199,1000)(200,999)(201,998)(202,997)(203,996)(204,995)(205,994)(206,993)(207,992)(208,991)(209,990)(210,989)(211,988)(212,987)(213,986)(214,985)(215,984)(216,983)(217,982)(218,981)(219,980)(220,979)(221,978)(222,977)(223,976)(224,975)(225,974)(226,973)(227,972)(228,971)(229,970)(230,969)(231,968)(232,967)(233,966)(234,965)(235,964)(236,963)(237,962)(238,961)(239,960)(240,959)(241,958)(242,957)(243,956)(244,955)(245,954)(246,953)(247,952)(248,951)(249,950)(250,949)(251,948)(252,947)(253,946)(254,945)(255,944)(256,943)(257,942)(258,941)(259,940)(260,939)(261,938)(262,937)(263,936)(264,935)(265,934)(266,933)(267,932)(268,931)(269,930)(270,929)(271,928)(272,927)(273,926)(274,925)(275,924)(276,923)(277,922)(278,921)(279,920)(280,919)(281,918)(282,917)(283,916)(284,915)(285,914)(286,913)(287,912)(288,911)(289,910)(290,909)(291,908)(292,907)(293,906)(294,905)(295,904)(296,903)(297,902)(298,901)(299,900)(300,899)(301,898)(302,897)(303,896)(304,895)(305,894)(306,893)(307,892)(308,891)(309,890)(310,889)(311,888)(312,887)(313,886)(314,885)(315,884)(316,883)(317,882)(318,881)(319,880)(320,879)(321,878)(322,877)(323,876)(324,875)(325,874)(326,873)(327,872)(328,871)(329,870)(330,869)(331,868)(332,867)(333,866)(334,865)(335,864)(336,863)(337,862)(338,861)(339,860)(340,859)(341,858)(342,857)(343,856)(344,855)(345,854)(346,853)(347,852)(348,851)(349,850)(350,849)(351,848)(352,847)(353,846)(354,845)(355,844)(356,843)(357,842)(358,841)(359,840)(360,839)(361,838)(362,837)(363,836)(364,835)(365,834)(366,833)(367,832)(368,831)(369,830)(370,829)(371,828)(372,827)(373,826)(374,825)(375,824)(376,823)(377,822)(378,821)(379,820)(380,819)(381,818)(382,817)(383,816)(384,815)(385,814)(386,813)(387,812)(388,811)(389,810)(390,809)(391,808)(392,807)(393,806)(394,805)(395,804)(396,803)(397,802)(398,801)(399,800)(400,799)(401,798)(402,797)(403,796)(404,795)(405,794)(406,793)(407,792)(408,791)(409,790)(410,789)(411,788)(412,787)(413,786)(414,785)(415,784)(416,783)(417,782)(418,781)(419,780)(420,779)(421,778)(422,777)(423,776)(424,775)(425,774)(426,773)(427,772)(428,771)(429,770)(430,769)(431,768)(432,767)(433,766)(434,765)(435,764)(436,763)(437,762)(438,761)(439,760)(440,759)(441,758)(442,757)(443,756)(444,755)(445,754)(446,753)(447,752)(448,751)(449,750)(450,749)(451,748)(452,747)(453,746)(454,745)(455,744)(456,743)(457,742)(458,741)(459,740)(460,739)(461,738)(462,737)(463,736)(464,735)(465,734)(466,733)(467,732)(468,731)(469,730)(470,729)(471,728)(472,727)(473,726)(474,725)(475,724)(476,723)(477,722)(478,721)(479,720)(480,719)(481,718)(482,717)(483,716)(484,715)(485,714)(486,713)(487,712)(488,711)(489,710)(490,709)(491,708)(492,707)(493,706)(494,705)(495,704)(496,703)(497,702)(498,701)(499,700)(500,699)(501,698)(502,697)(503,696)(504,695)(505,694)(506,693)(507,692)(508,691)(509,690)(510,689)(511,688)(512,687)(513,686)(514,685)(515,684)(516,683)(517,682)(518,681)(519,680)(520,679)(521,678)(522,677)(523,676)(524,675)(525,674)(526,673)(527,672)(528,671)(529,670)(530,669)(531,668)(532,667)(533,666)(534,665)(535,664)(536,663)(537,662)(538,661)(539,660)(540,659)(541,658)(542,657)(543,656)(544,655)(545,654)(546,653)(547,652)(548,651)(549,650)(550,649)(551,648)(552,647)(553,646)(554,645)(555,644)(556,643)(557,642)(558,641)(559,640)(560,639)(561,638)(562,637)(563,636)(564,635)(565,634)(566,633)(567,632)(568,631)(569,630)(570,629)(571,628)(572,627)(573,626)(574,625)(575,624)(576,623)(577,622)(578,621)(579,620)(580,619)(581,618)(582,617)(583,616)(584,615)(585,614)(586,613)(587,612)(588,611)(589,610)(590,609)(591,608)(592,607)(593,606)(594,605)(595,604)(596,603)(597,602)(598,601)(599,600)
Polycyclic presentation:
2^4,1181|c^2=d,b^a=bc,c^a=cd,e^a=e^1180,c^b=cd,e^b=e^1180
Conjugacy classes & character table
4727 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18896, 26);
Finite Group Databasebeta