D₃₀₂₁₁ #68738799

order	60422
automorphism	Aut(G) order 912674310
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral

D₃₀₂₁₁

Splittings

Fitting, socle, derived, Sylow

C₃₀₂₁₁ ⋊ C₂

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃₀₂₁₁	C₂
LCS	G ▷ C₃₀₂₁₁
UCS	C₁

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 30211
transitive degree	μ_t(G) = 30211

A minimal faithful permutation representation — 2 generators on 30211 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1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524)(14690,15523)(14691,15522)(14692,15521)(14693,15520)(14694,15519)(14695,15518)(14696,15517)(14697,15516)(14698,15515)(14699,15514)(14700,15513)(14701,15512)(14702,15511)(14703,15510)(14704,15509)(14705,15508)(14706,15507)(14707,15506)(14708,15505)(14709,15504)(14710,15503)(14711,15502)(14712,15501)(14713,15500)(14714,15499)(14715,15498)(14716,15497)(14717,15496)(14718,15495)(14719,15494)(14720,15493)(14721,15492)(14722,15491)(14723,15490)(14724,15489)(14725,15488)(14726,15487)(14727,15486)(14728,15485)(14729,15484)(14730,15483)(14731,15482)(14732,15481)(14733,15480)(14734,15479)(14735,15478)(14736,15477)(14737,15476)(14738,15475)(14739,15474)(14740,15473)(14741,15472)(14742,15471)(14743,15470)(14744,15469)(14745,15468)(14746,15467)(14747,15466)(14748,15465)(14749,15464)(14750,15463)(14751,15462)(14752,15461)(14753,15460)(14754,15459)(14755,15458)(14756,15457)(14757,15456)(14758,15455)(14759,15454)(14760,15453)(14761,15452)(14762,15451)(14763,15450)(14764,15449)(14765,15448)(14766,15447)(14767,15446)(14768,15445)(14769,15444)(14770,15443)(14771,15442)(14772,15441)(14773,15440)(14774,15439)(14775,15438)(14776,15437)(14777,15436)(14778,15435)(14779,15434)(14780,15433)(14781,15432)(14782,15431)(14783,15430)(14784,15429)(14785,15428)(14786,15427)(14787,15426)(14788,15425)(14789,15424)(14790,15423)(14791,15422)(14792,15421)(14793,15420)(14794,15419)(14795,15418)(14796,15417)(14797,15416)(14798,15415)(14799,15414)(14800,15413)(14801,15412)(14802,15411)(14803,15410)(14804,15409)(14805,15408)(14806,15407)(14807,15406)(14808,15405)(14809,15404)(14810,15403)(14811,15402)(14812,15401)(14813,15400)(14814,15399)(14815,15398)(14816,15397)(14817,15396)(14818,15395)(14819,15394)(14820,15393)(14821,15392)(14822,15391)(14823,15390)(14824,15389)(14825,15388)(14826,15387)(14827,15386)(14828,15385)(14829,15384)(14830,15383)(14831,15382)(14832,15381)(14833,15380)(14834,15379)(14835,15378)(14836,15377)(14837,15376)(14838,15375)(14839,15374)(14840,15373)(14841,15372)(14842,15371)(14843,15370)(14844,15369)(14845,15368)(14846,15367)(14847,15366)(14848,15365)(14849,15364)(14850,15363)(14851,15362)(14852,15361)(14853,15360)(14854,15359)(14855,15358)(14856,15357)(14857,15356)(14858,15355)(14859,15354)(14860,15353)(14861,15352)(14862,15351)(14863,15350)(14864,15349)(14865,15348)(14866,15347)(14867,15346)(14868,15345)(14869,15344)(14870,15343)(14871,15342)(14872,15341)(14873,15340)(14874,15339)(14875,15338)(14876,15337)(14877,15336)(14878,15335)(14879,15334)(14880,15333)(14881,15332)(14882,15331)(14883,15330)(14884,15329)(14885,15328)(14886,15327)(14887,15326)(14888,15325)(14889,15324)(14890,15323)(14891,15322)(14892,15321)(14893,15320)(14894,15319)(14895,15318)(14896,15317)(14897,15316)(14898,15315)(14899,15314)(14900,15313)(14901,15312)(14902,15311)(14903,15310)(14904,15309)(14905,15308)(14906,15307)(14907,15306)(14908,15305)(14909,15304)(14910,15303)(14911,15302)(14912,15301)(14913,15300)(14914,15299)(14915,15298)(14916,15297)(14917,15296)(14918,15295)(14919,15294)(14920,15293)(14921,15292)(14922,15291)(14923,15290)(14924,15289)(14925,15288)(14926,15287)(14927,15286)(14928,15285)(14929,15284)(14930,15283)(14931,15282)(14932,15281)(14933,15280)(14934,15279)(14935,15278)(14936,15277)(14937,15276)(14938,15275)(14939,15274)(14940,15273)(14941,15272)(14942,15271)(14943,15270)(14944,15269)(14945,15268)(14946,15267)(14947,15266)(14948,15265)(14949,15264)(14950,15263)(14951,15262)(14952,15261)(14953,15260)(14954,15259)(14955,15258)(14956,15257)(14957,15256)(14958,15255)(14959,15254)(14960,15253)(14961,15252)(14962,15251)(14963,15250)(14964,15249)(14965,15248)(14966,15247)(14967,15246)(14968,15245)(14969,15244)(14970,15243)(14971,15242)(14972,15241)(14973,15240)(14974,15239)(14975,15238)(14976,15237)(14977,15236)(14978,15235)(14979,15234)(14980,15233)(14981,15232)(14982,15231)(14983,15230)(14984,15229)(14985,15228)(14986,15227)(14987,15226)(14988,15225)(14989,15224)(14990,15223)(14991,15222)(14992,15221)(14993,15220)(14994,15219)(14995,15218)(14996,15217)(14997,15216)(14998,15215)(14999,15214)(15000,15213)(15001,15212)(15002,15211)(15003,15210)(15004,15209)(15005,15208)(15006,15207)(15007,15206)(15008,15205)(15009,15204)(15010,15203)(15011,15202)(15012,15201)(15013,15200)(15014,15199)(15015,15198)(15016,15197)(15017,15196)(15018,15195)(15019,15194)(15020,15193)(15021,15192)(15022,15191)(15023,15190)(15024,15189)(15025,15188)(15026,15187)(15027,15186)(15028,15185)(15029,15184)(15030,15183)(15031,15182)(15032,15181)(15033,15180)(15034,15179)(15035,15178)(15036,15177)(15037,15176)(15038,15175)(15039,15174)(15040,15173)(15041,15172)(15042,15171)(15043,15170)(15044,15169)(15045,15168)(15046,15167)(15047,15166)(15048,15165)(15049,15164)(15050,15163)(15051,15162)(15052,15161)(15053,15160)(15054,15159)(15055,15158)(15056,15157)(15057,15156)(15058,15155)(15059,15154)(15060,15153)(15061,15152)(15062,15151)(15063,15150)(15064,15149)(15065,15148)(15066,15147)(15067,15146)(15068,15145)(15069,15144)(15070,15143)(15071,15142)(15072,15141)(15073,15140)(15074,15139)(15075,15138)(15076,15137)(15077,15136)(15078,15135)(15079,15134)(15080,15133)(15081,15132)(15082,15131)(15083,15130)(15084,15129)(15085,15128)(15086,15127)(15087,15126)(15088,15125)(15089,15124)(15090,15123)(15091,15122)(15092,15121)(15093,15120)(15094,15119)(15095,15118)(15096,15117)(15097,15116)(15098,15115)(15099,15114)(15100,15113)(15101,15112)(15102,15111)(15103,15110)(15104,15109)(15105,15108)(15106,15107)

Polycyclic presentation:

2,30211|b^a=b^30210

Conjugacy classes & character table

15107 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(60422, 1);

D30211 #68738799