D₁₇₄₂₉ #46852809

order	34858
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₇₄₂₉
unambiguous semidirect product	C₂₉⋊D₆₀₁
unambiguous semidirect product	C₆₀₁⋊D₂₉

Splittings

Fitting, socle, derived, Hall	C₂₉×C₆₀₁ ⋊ C₂
Sylow	C₆₀₁ ⋊ D₂₉
Sylow	C₂₉ ⋊ D₆₀₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂₉×C₆₀₁	C₂
LCS	G ▷ C₂₉×C₆₀₁
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 630
transitive degree	μ_t(G) = 17429

A minimal faithful permutation representation — 2 generators on 630 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);(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(31,630)(32,629)(33,628)(34,627)(35,626)(36,625)(37,624)(38,623)(39,622)(40,621)(41,620)(42,619)(43,618)(44,617)(45,616)(46,615)(47,614)(48,613)(49,612)(50,611)(51,610)(52,609)(53,608)(54,607)(55,606)(56,605)(57,604)(58,603)(59,602)(60,601)(61,600)(62,599)(63,598)(64,597)(65,596)(66,595)(67,594)(68,593)(69,592)(70,591)(71,590)(72,589)(73,588)(74,587)(75,586)(76,585)(77,584)(78,583)(79,582)(80,581)(81,580)(82,579)(83,578)(84,577)(85,576)(86,575)(87,574)(88,573)(89,572)(90,571)(91,570)(92,569)(93,568)(94,567)(95,566)(96,565)(97,564)(98,563)(99,562)(100,561)(101,560)(102,559)(103,558)(104,557)(105,556)(106,555)(107,554)(108,553)(109,552)(110,551)(111,550)(112,549)(113,548)(114,547)(115,546)(116,545)(117,544)(118,543)(119,542)(120,541)(121,540)(122,539)(123,538)(124,537)(125,536)(126,535)(127,534)(128,533)(129,532)(130,531)(131,530)(132,529)(133,528)(134,527)(135,526)(136,525)(137,524)(138,523)(139,522)(140,521)(141,520)(142,519)(143,518)(144,517)(145,516)(146,515)(147,514)(148,513)(149,512)(150,511)(151,510)(152,509)(153,508)(154,507)(155,506)(156,505)(157,504)(158,503)(159,502)(160,501)(161,500)(162,499)(163,498)(164,497)(165,496)(166,495)(167,494)(168,493)(169,492)(170,491)(171,490)(172,489)(173,488)(174,487)(175,486)(176,485)(177,484)(178,483)(179,482)(180,481)(181,480)(182,479)(183,478)(184,477)(185,476)(186,475)(187,474)(188,473)(189,472)(190,471)(191,470)(192,469)(193,468)(194,467)(195,466)(196,465)(197,464)(198,463)(199,462)(200,461)(201,460)(202,459)(203,458)(204,457)(205,456)(206,455)(207,454)(208,453)(209,452)(210,451)(211,450)(212,449)(213,448)(214,447)(215,446)(216,445)(217,444)(218,443)(219,442)(220,441)(221,440)(222,439)(223,438)(224,437)(225,436)(226,435)(227,434)(228,433)(229,432)(230,431)(231,430)(232,429)(233,428)(234,427)(235,426)(236,425)(237,424)(238,423)(239,422)(240,421)(241,420)(242,419)(243,418)(244,417)(245,416)(246,415)(247,414)(248,413)(249,412)(250,411)(251,410)(252,409)(253,408)(254,407)(255,406)(256,405)(257,404)(258,403)(259,402)(260,401)(261,400)(262,399)(263,398)(264,397)(265,396)(266,395)(267,394)(268,393)(269,392)(270,391)(271,390)(272,389)(273,388)(274,387)(275,386)(276,385)(277,384)(278,383)(279,382)(280,381)(281,380)(282,379)(283,378)(284,377)(285,376)(286,375)(287,374)(288,373)(289,372)(290,371)(291,370)(292,369)(293,368)(294,367)(295,366)(296,365)(297,364)(298,363)(299,362)(300,361)(301,360)(302,359)(303,358)(304,357)(305,356)(306,355)(307,354)(308,353)(309,352)(310,351)(311,350)(312,349)(313,348)(314,347)(315,346)(316,345)(317,344)(318,343)(319,342)(320,341)(321,340)(322,339)(323,338)(324,337)(325,336)(326,335)(327,334)(328,333)(329,332)(330,331)

Polycyclic presentation:

2,29,601|b^a=b^28,c^a=c^600

Conjugacy classes & character table

8716 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34858, 3);

D17429 #46852809