C₂×D₈₈₄₇ #47978144

order	35388
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₇₆₉₄
direct product	C₂×D₈₈₄₇
unambiguous semidirect product	(C₂×C₉)⋊D₉₈₃
unambiguous semidirect product	(C₂×C₉₈₃)⋊D₉

Splittings

Fitting	C₂×C₉×C₉₈₃ ⋊ C₂
derived, Hall	C₉×C₉₈₃ ⋊ C₂²
Sylow	C₉₈₃ ⋊ C₂×D₉
Sylow	C₉ ⋊ C₂×D₉₈₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₈₈₄₇
commutator, cosocle, hypocenter	C₉×C₉₈₃	C₂²
Frattini	C₃	C₂×D₂₉₄₉
Fitting	C₂×C₉×C₉₈₃	C₂
socle	C₂×C₃×C₉₈₃	D₃
LCS	G ▷ C₉×C₉₈₃
UCS	C₁ ◁ C₂

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 994
transitive degree	μ_t(G) = 17694

A minimal faithful permutation representation — 2 generators on 994 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);(4,11)(5,10)(6,9)(7,8)(13,994)(14,993)(15,992)(16,991)(17,990)(18,989)(19,988)(20,987)(21,986)(22,985)(23,984)(24,983)(25,982)(26,981)(27,980)(28,979)(29,978)(30,977)(31,976)(32,975)(33,974)(34,973)(35,972)(36,971)(37,970)(38,969)(39,968)(40,967)(41,966)(42,965)(43,964)(44,963)(45,962)(46,961)(47,960)(48,959)(49,958)(50,957)(51,956)(52,955)(53,954)(54,953)(55,952)(56,951)(57,950)(58,949)(59,948)(60,947)(61,946)(62,945)(63,944)(64,943)(65,942)(66,941)(67,940)(68,939)(69,938)(70,937)(71,936)(72,935)(73,934)(74,933)(75,932)(76,931)(77,930)(78,929)(79,928)(80,927)(81,926)(82,925)(83,924)(84,923)(85,922)(86,921)(87,920)(88,919)(89,918)(90,917)(91,916)(92,915)(93,914)(94,913)(95,912)(96,911)(97,910)(98,909)(99,908)(100,907)(101,906)(102,905)(103,904)(104,903)(105,902)(106,901)(107,900)(108,899)(109,898)(110,897)(111,896)(112,895)(113,894)(114,893)(115,892)(116,891)(117,890)(118,889)(119,888)(120,887)(121,886)(122,885)(123,884)(124,883)(125,882)(126,881)(127,880)(128,879)(129,878)(130,877)(131,876)(132,875)(133,874)(134,873)(135,872)(136,871)(137,870)(138,869)(139,868)(140,867)(141,866)(142,865)(143,864)(144,863)(145,862)(146,861)(147,860)(148,859)(149,858)(150,857)(151,856)(152,855)(153,854)(154,853)(155,852)(156,851)(157,850)(158,849)(159,848)(160,847)(161,846)(162,845)(163,844)(164,843)(165,842)(166,841)(167,840)(168,839)(169,838)(170,837)(171,836)(172,835)(173,834)(174,833)(175,832)(176,831)(177,830)(178,829)(179,828)(180,827)(181,826)(182,825)(183,824)(184,823)(185,822)(186,821)(187,820)(188,819)(189,818)(190,817)(191,816)(192,815)(193,814)(194,813)(195,812)(196,811)(197,810)(198,809)(199,808)(200,807)(201,806)(202,805)(203,804)(204,803)(205,802)(206,801)(207,800)(208,799)(209,798)(210,797)(211,796)(212,795)(213,794)(214,793)(215,792)(216,791)(217,790)(218,789)(219,788)(220,787)(221,786)(222,785)(223,784)(224,783)(225,782)(226,781)(227,780)(228,779)(229,778)(230,777)(231,776)(232,775)(233,774)(234,773)(235,772)(236,771)(237,770)(238,769)(239,768)(240,767)(241,766)(242,765)(243,764)(244,763)(245,762)(246,761)(247,760)(248,759)(249,758)(250,757)(251,756)(252,755)(253,754)(254,753)(255,752)(256,751)(257,750)(258,749)(259,748)(260,747)(261,746)(262,745)(263,744)(264,743)(265,742)(266,741)(267,740)(268,739)(269,738)(270,737)(271,736)(272,735)(273,734)(274,733)(275,732)(276,731)(277,730)(278,729)(279,728)(280,727)(281,726)(282,725)(283,724)(284,723)(285,722)(286,721)(287,720)(288,719)(289,718)(290,717)(291,716)(292,715)(293,714)(294,713)(295,712)(296,711)(297,710)(298,709)(299,708)(300,707)(301,706)(302,705)(303,704)(304,703)(305,702)(306,701)(307,700)(308,699)(309,698)(310,697)(311,696)(312,695)(313,694)(314,693)(315,692)(316,691)(317,690)(318,689)(319,688)(320,687)(321,686)(322,685)(323,684)(324,683)(325,682)(326,681)(327,680)(328,679)(329,678)(330,677)(331,676)(332,675)(333,674)(334,673)(335,672)(336,671)(337,670)(338,669)(339,668)(340,667)(341,666)(342,665)(343,664)(344,663)(345,662)(346,661)(347,660)(348,659)(349,658)(350,657)(351,656)(352,655)(353,654)(354,653)(355,652)(356,651)(357,650)(358,649)(359,648)(360,647)(361,646)(362,645)(363,644)(364,643)(365,642)(366,641)(367,640)(368,639)(369,638)(370,637)(371,636)(372,635)(373,634)(374,633)(375,632)(376,631)(377,630)(378,629)(379,628)(380,627)(381,626)(382,625)(383,624)(384,623)(385,622)(386,621)(387,620)(388,619)(389,618)(390,617)(391,616)(392,615)(393,614)(394,613)(395,612)(396,611)(397,610)(398,609)(399,608)(400,607)(401,606)(402,605)(403,604)(404,603)(405,602)(406,601)(407,600)(408,599)(409,598)(410,597)(411,596)(412,595)(413,594)(414,593)(415,592)(416,591)(417,590)(418,589)(419,588)(420,587)(421,586)(422,585)(423,584)(424,583)(425,582)(426,581)(427,580)(428,579)(429,578)(430,577)(431,576)(432,575)(433,574)(434,573)(435,572)(436,571)(437,570)(438,569)(439,568)(440,567)(441,566)(442,565)(443,564)(444,563)(445,562)(446,561)(447,560)(448,559)(449,558)(450,557)(451,556)(452,555)(453,554)(454,553)(455,552)(456,551)(457,550)(458,549)(459,548)(460,547)(461,546)(462,545)(463,544)(464,543)(465,542)(466,541)(467,540)(468,539)(469,538)(470,537)(471,536)(472,535)(473,534)(474,533)(475,532)(476,531)(477,530)(478,529)(479,528)(480,527)(481,526)(482,525)(483,524)(484,523)(485,522)(486,521)(487,520)(488,519)(489,518)(490,517)(491,516)(492,515)(493,514)(494,513)(495,512)(496,511)(497,510)(498,509)(499,508)(500,507)(501,506)(502,505)(503,504)

Conjugacy classes & character table

8850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35388, 8);

C2×D8847 #47978144