C₂×D₃₆₀₃ #28385688

order	14412
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₇₂₀₆
direct product	C₂×D₃₆₀₃
unambiguous semidirect product	(C₂×C₃)⋊D₁₂₀₁
unambiguous semidirect product	(C₂×C₁₂₀₁)⋊D₃

Splittings

Fitting, socle	C₂×C₃×C₁₂₀₁ ⋊ C₂
derived, Hall	C₃×C₁₂₀₁ ⋊ C₂²
Sylow	C₁₂₀₁ ⋊ C₂×D₃
Sylow	C₃ ⋊ C₂×D₁₂₀₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₃₆₀₃
commutator, cosocle, hypocenter	C₃×C₁₂₀₁	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₂₀₁	C₂
LCS	G ▷ C₃×C₁₂₀₁
UCS	C₁ ◁ C₂

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1206
transitive degree	μ_t(G) = 7206

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

Conjugacy classes & character table

3606 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₁₄₄₁₂
maximal normal subgroup of	D₁₄₄₁₂
maximal quotient of	D₁₄₄₁₂, Dic₇₂₀₆

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14412, 16);

C2×D3603 #28385688