Finite Group DatabasebetaFinite Group Databasebeta| order | 34822 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D17411 |
| unambiguous semidirect product | C23⋊D757 |
| unambiguous semidirect product | C757⋊D23 |
| Fitting, socle, derived, Hall | C23×C757 ⋊ C2 |
| Sylow | C757 ⋊ D23 |
| Sylow | C23 ⋊ D757 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C757 | C2 |
| LCS | G ▷ C23×C757 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 780 |
| transitive degree | μt(G) = 17411 |
A minimal faithful permutation representation — 2 generators on 780 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);(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)(25,780)(26,779)(27,778)(28,777)(29,776)(30,775)(31,774)(32,773)(33,772)(34,771)(35,770)(36,769)(37,768)(38,767)(39,766)(40,765)(41,764)(42,763)(43,762)(44,761)(45,760)(46,759)(47,758)(48,757)(49,756)(50,755)(51,754)(52,753)(53,752)(54,751)(55,750)(56,749)(57,748)(58,747)(59,746)(60,745)(61,744)(62,743)(63,742)(64,741)(65,740)(66,739)(67,738)(68,737)(69,736)(70,735)(71,734)(72,733)(73,732)(74,731)(75,730)(76,729)(77,728)(78,727)(79,726)(80,725)(81,724)(82,723)(83,722)(84,721)(85,720)(86,719)(87,718)(88,717)(89,716)(90,715)(91,714)(92,713)(93,712)(94,711)(95,710)(96,709)(97,708)(98,707)(99,706)(100,705)(101,704)(102,703)(103,702)(104,701)(105,700)(106,699)(107,698)(108,697)(109,696)(110,695)(111,694)(112,693)(113,692)(114,691)(115,690)(116,689)(117,688)(118,687)(119,686)(120,685)(121,684)(122,683)(123,682)(124,681)(125,680)(126,679)(127,678)(128,677)(129,676)(130,675)(131,674)(132,673)(133,672)(134,671)(135,670)(136,669)(137,668)(138,667)(139,666)(140,665)(141,664)(142,663)(143,662)(144,661)(145,660)(146,659)(147,658)(148,657)(149,656)(150,655)(151,654)(152,653)(153,652)(154,651)(155,650)(156,649)(157,648)(158,647)(159,646)(160,645)(161,644)(162,643)(163,642)(164,641)(165,640)(166,639)(167,638)(168,637)(169,636)(170,635)(171,634)(172,633)(173,632)(174,631)(175,630)(176,629)(177,628)(178,627)(179,626)(180,625)(181,624)(182,623)(183,622)(184,621)(185,620)(186,619)(187,618)(188,617)(189,616)(190,615)(191,614)(192,613)(193,612)(194,611)(195,610)(196,609)(197,608)(198,607)(199,606)(200,605)(201,604)(202,603)(203,602)(204,601)(205,600)(206,599)(207,598)(208,597)(209,596)(210,595)(211,594)(212,593)(213,592)(214,591)(215,590)(216,589)(217,588)(218,587)(219,586)(220,585)(221,584)(222,583)(223,582)(224,581)(225,580)(226,579)(227,578)(228,577)(229,576)(230,575)(231,574)(232,573)(233,572)(234,571)(235,570)(236,569)(237,568)(238,567)(239,566)(240,565)(241,564)(242,563)(243,562)(244,561)(245,560)(246,559)(247,558)(248,557)(249,556)(250,555)(251,554)(252,553)(253,552)(254,551)(255,550)(256,549)(257,548)(258,547)(259,546)(260,545)(261,544)(262,543)(263,542)(264,541)(265,540)(266,539)(267,538)(268,537)(269,536)(270,535)(271,534)(272,533)(273,532)(274,531)(275,530)(276,529)(277,528)(278,527)(279,526)(280,525)(281,524)(282,523)(283,522)(284,521)(285,520)(286,519)(287,518)(288,517)(289,516)(290,515)(291,514)(292,513)(293,512)(294,511)(295,510)(296,509)(297,508)(298,507)(299,506)(300,505)(301,504)(302,503)(303,502)(304,501)(305,500)(306,499)(307,498)(308,497)(309,496)(310,495)(311,494)(312,493)(313,492)(314,491)(315,490)(316,489)(317,488)(318,487)(319,486)(320,485)(321,484)(322,483)(323,482)(324,481)(325,480)(326,479)(327,478)(328,477)(329,476)(330,475)(331,474)(332,473)(333,472)(334,471)(335,470)(336,469)(337,468)(338,467)(339,466)(340,465)(341,464)(342,463)(343,462)(344,461)(345,460)(346,459)(347,458)(348,457)(349,456)(350,455)(351,454)(352,453)(353,452)(354,451)(355,450)(356,449)(357,448)(358,447)(359,446)(360,445)(361,444)(362,443)(363,442)(364,441)(365,440)(366,439)(367,438)(368,437)(369,436)(370,435)(371,434)(372,433)(373,432)(374,431)(375,430)(376,429)(377,428)(378,427)(379,426)(380,425)(381,424)(382,423)(383,422)(384,421)(385,420)(386,419)(387,418)(388,417)(389,416)(390,415)(391,414)(392,413)(393,412)(394,411)(395,410)(396,409)(397,408)(398,407)(399,406)(400,405)(401,404)(402,403)Polycyclic presentation:
2,23,757|b^a=b^22,c^a=c^7568707 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34822, 3);