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D9544 #34061791
Aliases
Splittings
Subgroups
22 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1201 points:
(1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201);(2,8)(3,7)(4,6)(10,1201)(11,1200)(12,1199)(13,1198)(14,1197)(15,1196)(16,1195)(17,1194)(18,1193)(19,1192)(20,1191)(21,1190)(22,1189)(23,1188)(24,1187)(25,1186)(26,1185)(27,1184)(28,1183)(29,1182)(30,1181)(31,1180)(32,1179)(33,1178)(34,1177)(35,1176)(36,1175)(37,1174)(38,1173)(39,1172)(40,1171)(41,1170)(42,1169)(43,1168)(44,1167)(45,1166)(46,1165)(47,1164)(48,1163)(49,1162)(50,1161)(51,1160)(52,1159)(53,1158)(54,1157)(55,1156)(56,1155)(57,1154)(58,1153)(59,1152)(60,1151)(61,1150)(62,1149)(63,1148)(64,1147)(65,1146)(66,1145)(67,1144)(68,1143)(69,1142)(70,1141)(71,1140)(72,1139)(73,1138)(74,1137)(75,1136)(76,1135)(77,1134)(78,1133)(79,1132)(80,1131)(81,1130)(82,1129)(83,1128)(84,1127)(85,1126)(86,1125)(87,1124)(88,1123)(89,1122)(90,1121)(91,1120)(92,1119)(93,1118)(94,1117)(95,1116)(96,1115)(97,1114)(98,1113)(99,1112)(100,1111)(101,1110)(102,1109)(103,1108)(104,1107)(105,1106)(106,1105)(107,1104)(108,1103)(109,1102)(110,1101)(111,1100)(112,1099)(113,1098)(114,1097)(115,1096)(116,1095)(117,1094)(118,1093)(119,1092)(120,1091)(121,1090)(122,1089)(123,1088)(124,1087)(125,1086)(126,1085)(127,1084)(128,1083)(129,1082)(130,1081)(131,1080)(132,1079)(133,1078)(134,1077)(135,1076)(136,1075)(137,1074)(138,1073)(139,1072)(140,1071)(141,1070)(142,1069)(143,1068)(144,1067)(145,1066)(146,1065)(147,1064)(148,1063)(149,1062)(150,1061)(151,1060)(152,1059)(153,1058)(154,1057)(155,1056)(156,1055)(157,1054)(158,1053)(159,1052)(160,1051)(161,1050)(162,1049)(163,1048)(164,1047)(165,1046)(166,1045)(167,1044)(168,1043)(169,1042)(170,1041)(171,1040)(172,1039)(173,1038)(174,1037)(175,1036)(176,1035)(177,1034)(178,1033)(179,1032)(180,1031)(181,1030)(182,1029)(183,1028)(184,1027)(185,1026)(186,1025)(187,1024)(188,1023)(189,1022)(190,1021)(191,1020)(192,1019)(193,1018)(194,1017)(195,1016)(196,1015)(197,1014)(198,1013)(199,1012)(200,1011)(201,1010)(202,1009)(203,1008)(204,1007)(205,1006)(206,1005)(207,1004)(208,1003)(209,1002)(210,1001)(211,1000)(212,999)(213,998)(214,997)(215,996)(216,995)(217,994)(218,993)(219,992)(220,991)(221,990)(222,989)(223,988)(224,987)(225,986)(226,985)(227,984)(228,983)(229,982)(230,981)(231,980)(232,979)(233,978)(234,977)(235,976)(236,975)(237,974)(238,973)(239,972)(240,971)(241,970)(242,969)(243,968)(244,967)(245,966)(246,965)(247,964)(248,963)(249,962)(250,961)(251,960)(252,959)(253,958)(254,957)(255,956)(256,955)(257,954)(258,953)(259,952)(260,951)(261,950)(262,949)(263,948)(264,947)(265,946)(266,945)(267,944)(268,943)(269,942)(270,941)(271,940)(272,939)(273,938)(274,937)(275,936)(276,935)(277,934)(278,933)(279,932)(280,931)(281,930)(282,929)(283,928)(284,927)(285,926)(286,925)(287,924)(288,923)(289,922)(290,921)(291,920)(292,919)(293,918)(294,917)(295,916)(296,915)(297,914)(298,913)(299,912)(300,911)(301,910)(302,909)(303,908)(304,907)(305,906)(306,905)(307,904)(308,903)(309,902)(310,901)(311,900)(312,899)(313,898)(314,897)(315,896)(316,895)(317,894)(318,893)(319,892)(320,891)(321,890)(322,889)(323,888)(324,887)(325,886)(326,885)(327,884)(328,883)(329,882)(330,881)(331,880)(332,879)(333,878)(334,877)(335,876)(336,875)(337,874)(338,873)(339,872)(340,871)(341,870)(342,869)(343,868)(344,867)(345,866)(346,865)(347,864)(348,863)(349,862)(350,861)(351,860)(352,859)(353,858)(354,857)(355,856)(356,855)(357,854)(358,853)(359,852)(360,851)(361,850)(362,849)(363,848)(364,847)(365,846)(366,845)(367,844)(368,843)(369,842)(370,841)(371,840)(372,839)(373,838)(374,837)(375,836)(376,835)(377,834)(378,833)(379,832)(380,831)(381,830)(382,829)(383,828)(384,827)(385,826)(386,825)(387,824)(388,823)(389,822)(390,821)(391,820)(392,819)(393,818)(394,817)(395,816)(396,815)(397,814)(398,813)(399,812)(400,811)(401,810)(402,809)(403,808)(404,807)(405,806)(406,805)(407,804)(408,803)(409,802)(410,801)(411,800)(412,799)(413,798)(414,797)(415,796)(416,795)(417,794)(418,793)(419,792)(420,791)(421,790)(422,789)(423,788)(424,787)(425,786)(426,785)(427,784)(428,783)(429,782)(430,781)(431,780)(432,779)(433,778)(434,777)(435,776)(436,775)(437,774)(438,773)(439,772)(440,771)(441,770)(442,769)(443,768)(444,767)(445,766)(446,765)(447,764)(448,763)(449,762)(450,761)(451,760)(452,759)(453,758)(454,757)(455,756)(456,755)(457,754)(458,753)(459,752)(460,751)(461,750)(462,749)(463,748)(464,747)(465,746)(466,745)(467,744)(468,743)(469,742)(470,741)(471,740)(472,739)(473,738)(474,737)(475,736)(476,735)(477,734)(478,733)(479,732)(480,731)(481,730)(482,729)(483,728)(484,727)(485,726)(486,725)(487,724)(488,723)(489,722)(490,721)(491,720)(492,719)(493,718)(494,717)(495,716)(496,715)(497,714)(498,713)(499,712)(500,711)(501,710)(502,709)(503,708)(504,707)(505,706)(506,705)(507,704)(508,703)(509,702)(510,701)(511,700)(512,699)(513,698)(514,697)(515,696)(516,695)(517,694)(518,693)(519,692)(520,691)(521,690)(522,689)(523,688)(524,687)(525,686)(526,685)(527,684)(528,683)(529,682)(530,681)(531,680)(532,679)(533,678)(534,677)(535,676)(536,675)(537,674)(538,673)(539,672)(540,671)(541,670)(542,669)(543,668)(544,667)(545,666)(546,665)(547,664)(548,663)(549,662)(550,661)(551,660)(552,659)(553,658)(554,657)(555,656)(556,655)(557,654)(558,653)(559,652)(560,651)(561,650)(562,649)(563,648)(564,647)(565,646)(566,645)(567,644)(568,643)(569,642)(570,641)(571,640)(572,639)(573,638)(574,637)(575,636)(576,635)(577,634)(578,633)(579,632)(580,631)(581,630)(582,629)(583,628)(584,627)(585,626)(586,625)(587,624)(588,623)(589,622)(590,621)(591,620)(592,619)(593,618)(594,617)(595,616)(596,615)(597,614)(598,613)(599,612)(600,611)(601,610)(602,609)(603,608)(604,607)(605,606)
Polycyclic presentation:
2^4,1193|c^2=d,b^a=bc,c^a=cd,e^a=e^1192,c^b=cd,e^b=e^1192
Conjugacy classes & character table
4775 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19088, 26);
Finite Group Databasebeta