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Dic6065 #37566100
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1222 points:
(1,2)(3,4)(5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222);(1,3,2,4)(6,9)(7,8)(11,1222)(12,1221)(13,1220)(14,1219)(15,1218)(16,1217)(17,1216)(18,1215)(19,1214)(20,1213)(21,1212)(22,1211)(23,1210)(24,1209)(25,1208)(26,1207)(27,1206)(28,1205)(29,1204)(30,1203)(31,1202)(32,1201)(33,1200)(34,1199)(35,1198)(36,1197)(37,1196)(38,1195)(39,1194)(40,1193)(41,1192)(42,1191)(43,1190)(44,1189)(45,1188)(46,1187)(47,1186)(48,1185)(49,1184)(50,1183)(51,1182)(52,1181)(53,1180)(54,1179)(55,1178)(56,1177)(57,1176)(58,1175)(59,1174)(60,1173)(61,1172)(62,1171)(63,1170)(64,1169)(65,1168)(66,1167)(67,1166)(68,1165)(69,1164)(70,1163)(71,1162)(72,1161)(73,1160)(74,1159)(75,1158)(76,1157)(77,1156)(78,1155)(79,1154)(80,1153)(81,1152)(82,1151)(83,1150)(84,1149)(85,1148)(86,1147)(87,1146)(88,1145)(89,1144)(90,1143)(91,1142)(92,1141)(93,1140)(94,1139)(95,1138)(96,1137)(97,1136)(98,1135)(99,1134)(100,1133)(101,1132)(102,1131)(103,1130)(104,1129)(105,1128)(106,1127)(107,1126)(108,1125)(109,1124)(110,1123)(111,1122)(112,1121)(113,1120)(114,1119)(115,1118)(116,1117)(117,1116)(118,1115)(119,1114)(120,1113)(121,1112)(122,1111)(123,1110)(124,1109)(125,1108)(126,1107)(127,1106)(128,1105)(129,1104)(130,1103)(131,1102)(132,1101)(133,1100)(134,1099)(135,1098)(136,1097)(137,1096)(138,1095)(139,1094)(140,1093)(141,1092)(142,1091)(143,1090)(144,1089)(145,1088)(146,1087)(147,1086)(148,1085)(149,1084)(150,1083)(151,1082)(152,1081)(153,1080)(154,1079)(155,1078)(156,1077)(157,1076)(158,1075)(159,1074)(160,1073)(161,1072)(162,1071)(163,1070)(164,1069)(165,1068)(166,1067)(167,1066)(168,1065)(169,1064)(170,1063)(171,1062)(172,1061)(173,1060)(174,1059)(175,1058)(176,1057)(177,1056)(178,1055)(179,1054)(180,1053)(181,1052)(182,1051)(183,1050)(184,1049)(185,1048)(186,1047)(187,1046)(188,1045)(189,1044)(190,1043)(191,1042)(192,1041)(193,1040)(194,1039)(195,1038)(196,1037)(197,1036)(198,1035)(199,1034)(200,1033)(201,1032)(202,1031)(203,1030)(204,1029)(205,1028)(206,1027)(207,1026)(208,1025)(209,1024)(210,1023)(211,1022)(212,1021)(213,1020)(214,1019)(215,1018)(216,1017)(217,1016)(218,1015)(219,1014)(220,1013)(221,1012)(222,1011)(223,1010)(224,1009)(225,1008)(226,1007)(227,1006)(228,1005)(229,1004)(230,1003)(231,1002)(232,1001)(233,1000)(234,999)(235,998)(236,997)(237,996)(238,995)(239,994)(240,993)(241,992)(242,991)(243,990)(244,989)(245,988)(246,987)(247,986)(248,985)(249,984)(250,983)(251,982)(252,981)(253,980)(254,979)(255,978)(256,977)(257,976)(258,975)(259,974)(260,973)(261,972)(262,971)(263,970)(264,969)(265,968)(266,967)(267,966)(268,965)(269,964)(270,963)(271,962)(272,961)(273,960)(274,959)(275,958)(276,957)(277,956)(278,955)(279,954)(280,953)(281,952)(282,951)(283,950)(284,949)(285,948)(286,947)(287,946)(288,945)(289,944)(290,943)(291,942)(292,941)(293,940)(294,939)(295,938)(296,937)(297,936)(298,935)(299,934)(300,933)(301,932)(302,931)(303,930)(304,929)(305,928)(306,927)(307,926)(308,925)(309,924)(310,923)(311,922)(312,921)(313,920)(314,919)(315,918)(316,917)(317,916)(318,915)(319,914)(320,913)(321,912)(322,911)(323,910)(324,909)(325,908)(326,907)(327,906)(328,905)(329,904)(330,903)(331,902)(332,901)(333,900)(334,899)(335,898)(336,897)(337,896)(338,895)(339,894)(340,893)(341,892)(342,891)(343,890)(344,889)(345,888)(346,887)(347,886)(348,885)(349,884)(350,883)(351,882)(352,881)(353,880)(354,879)(355,878)(356,877)(357,876)(358,875)(359,874)(360,873)(361,872)(362,871)(363,870)(364,869)(365,868)(366,867)(367,866)(368,865)(369,864)(370,863)(371,862)(372,861)(373,860)(374,859)(375,858)(376,857)(377,856)(378,855)(379,854)(380,853)(381,852)(382,851)(383,850)(384,849)(385,848)(386,847)(387,846)(388,845)(389,844)(390,843)(391,842)(392,841)(393,840)(394,839)(395,838)(396,837)(397,836)(398,835)(399,834)(400,833)(401,832)(402,831)(403,830)(404,829)(405,828)(406,827)(407,826)(408,825)(409,824)(410,823)(411,822)(412,821)(413,820)(414,819)(415,818)(416,817)(417,816)(418,815)(419,814)(420,813)(421,812)(422,811)(423,810)(424,809)(425,808)(426,807)(427,806)(428,805)(429,804)(430,803)(431,802)(432,801)(433,800)(434,799)(435,798)(436,797)(437,796)(438,795)(439,794)(440,793)(441,792)(442,791)(443,790)(444,789)(445,788)(446,787)(447,786)(448,785)(449,784)(450,783)(451,782)(452,781)(453,780)(454,779)(455,778)(456,777)(457,776)(458,775)(459,774)(460,773)(461,772)(462,771)(463,770)(464,769)(465,768)(466,767)(467,766)(468,765)(469,764)(470,763)(471,762)(472,761)(473,760)(474,759)(475,758)(476,757)(477,756)(478,755)(479,754)(480,753)(481,752)(482,751)(483,750)(484,749)(485,748)(486,747)(487,746)(488,745)(489,744)(490,743)(491,742)(492,741)(493,740)(494,739)(495,738)(496,737)(497,736)(498,735)(499,734)(500,733)(501,732)(502,731)(503,730)(504,729)(505,728)(506,727)(507,726)(508,725)(509,724)(510,723)(511,722)(512,721)(513,720)(514,719)(515,718)(516,717)(517,716)(518,715)(519,714)(520,713)(521,712)(522,711)(523,710)(524,709)(525,708)(526,707)(527,706)(528,705)(529,704)(530,703)(531,702)(532,701)(533,700)(534,699)(535,698)(536,697)(537,696)(538,695)(539,694)(540,693)(541,692)(542,691)(543,690)(544,689)(545,688)(546,687)(547,686)(548,685)(549,684)(550,683)(551,682)(552,681)(553,680)(554,679)(555,678)(556,677)(557,676)(558,675)(559,674)(560,673)(561,672)(562,671)(563,670)(564,669)(565,668)(566,667)(567,666)(568,665)(569,664)(570,663)(571,662)(572,661)(573,660)(574,659)(575,658)(576,657)(577,656)(578,655)(579,654)(580,653)(581,652)(582,651)(583,650)(584,649)(585,648)(586,647)(587,646)(588,645)(589,644)(590,643)(591,642)(592,641)(593,640)(594,639)(595,638)(596,637)(597,636)(598,635)(599,634)(600,633)(601,632)(602,631)(603,630)(604,629)(605,628)(606,627)(607,626)(608,625)(609,624)(610,623)(611,622)(612,621)(613,620)(614,619)(615,618)(616,617)
Polycyclic presentation:
2,5,1213,2|a^2=d,b^a=b^4,c^a=c^1212
Conjugacy classes & character table
6068 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24260, 4);
Finite Group Databasebeta