Finite Group DatabasebetaFinite Group Databasebeta| order | 36116 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic9029 |
| derived, Sylow | C9029 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D9029 |
| commutator, hypocenter | C9029 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C9029 | C2 |
| LCS | G ▷ C9029 | |
| UCS | C1 ◁ C2 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 9033 |
| transitive degree | μt(G) = 36116 |
A minimal faithful permutation representation — 2 generators on 9033 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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759)(4281,4758)(4282,4757)(4283,4756)(4284,4755)(4285,4754)(4286,4753)(4287,4752)(4288,4751)(4289,4750)(4290,4749)(4291,4748)(4292,4747)(4293,4746)(4294,4745)(4295,4744)(4296,4743)(4297,4742)(4298,4741)(4299,4740)(4300,4739)(4301,4738)(4302,4737)(4303,4736)(4304,4735)(4305,4734)(4306,4733)(4307,4732)(4308,4731)(4309,4730)(4310,4729)(4311,4728)(4312,4727)(4313,4726)(4314,4725)(4315,4724)(4316,4723)(4317,4722)(4318,4721)(4319,4720)(4320,4719)(4321,4718)(4322,4717)(4323,4716)(4324,4715)(4325,4714)(4326,4713)(4327,4712)(4328,4711)(4329,4710)(4330,4709)(4331,4708)(4332,4707)(4333,4706)(4334,4705)(4335,4704)(4336,4703)(4337,4702)(4338,4701)(4339,4700)(4340,4699)(4341,4698)(4342,4697)(4343,4696)(4344,4695)(4345,4694)(4346,4693)(4347,4692)(4348,4691)(4349,4690)(4350,4689)(4351,4688)(4352,4687)(4353,4686)(4354,4685)(4355,4684)(4356,4683)(4357,4682)(4358,4681)(4359,4680)(4360,4679)(4361,4678)(4362,4677)(4363,4676)(4364,4675)(4365,4674)(4366,4673)(4367,4672)(4368,4671)(4369,4670)(4370,4669)(4371,4668)(4372,4667)(4373,4666)(4374,4665)(4375,4664)(4376,4663)(4377,4662)(4378,4661)(4379,4660)(4380,4659)(4381,4658)(4382,4657)(4383,4656)(4384,4655)(4385,4654)(4386,4653)(4387,4652)(4388,4651)(4389,4650)(4390,4649)(4391,4648)(4392,4647)(4393,4646)(4394,4645)(4395,4644)(4396,4643)(4397,4642)(4398,4641)(4399,4640)(4400,4639)(4401,4638)(4402,4637)(4403,4636)(4404,4635)(4405,4634)(4406,4633)(4407,4632)(4408,4631)(4409,4630)(4410,4629)(4411,4628)(4412,4627)(4413,4626)(4414,4625)(4415,4624)(4416,4623)(4417,4622)(4418,4621)(4419,4620)(4420,4619)(4421,4618)(4422,4617)(4423,4616)(4424,4615)(4425,4614)(4426,4613)(4427,4612)(4428,4611)(4429,4610)(4430,4609)(4431,4608)(4432,4607)(4433,4606)(4434,4605)(4435,4604)(4436,4603)(4437,4602)(4438,4601)(4439,4600)(4440,4599)(4441,4598)(4442,4597)(4443,4596)(4444,4595)(4445,4594)(4446,4593)(4447,4592)(4448,4591)(4449,4590)(4450,4589)(4451,4588)(4452,4587)(4453,4586)(4454,4585)(4455,4584)(4456,4583)(4457,4582)(4458,4581)(4459,4580)(4460,4579)(4461,4578)(4462,4577)(4463,4576)(4464,4575)(4465,4574)(4466,4573)(4467,4572)(4468,4571)(4469,4570)(4470,4569)(4471,4568)(4472,4567)(4473,4566)(4474,4565)(4475,4564)(4476,4563)(4477,4562)(4478,4561)(4479,4560)(4480,4559)(4481,4558)(4482,4557)(4483,4556)(4484,4555)(4485,4554)(4486,4553)(4487,4552)(4488,4551)(4489,4550)(4490,4549)(4491,4548)(4492,4547)(4493,4546)(4494,4545)(4495,4544)(4496,4543)(4497,4542)(4498,4541)(4499,4540)(4500,4539)(4501,4538)(4502,4537)(4503,4536)(4504,4535)(4505,4534)(4506,4533)(4507,4532)(4508,4531)(4509,4530)(4510,4529)(4511,4528)(4512,4527)(4513,4526)(4514,4525)(4515,4524)(4516,4523)(4517,4522)(4518,4521)(4519,4520)Polycyclic presentation:
2^2,9029|a^2=b,c^a=c^90289032 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36116, 1);