D₉₆₇₃ #34083997

order	19346
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₉₆₇₃
unambiguous semidirect product	C₁₇⋊D₅₆₉
unambiguous semidirect product	C₅₆₉⋊D₁₇

Splittings

Fitting, socle, derived, Hall	C₁₇×C₅₆₉ ⋊ C₂
Sylow	C₅₆₉ ⋊ D₁₇
Sylow	C₁₇ ⋊ D₅₆₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₇×C₅₆₉	C₂
LCS	G ▷ C₁₇×C₅₆₉
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 586
transitive degree	μ_t(G) = 9673

A minimal faithful permutation representation — 2 generators on 586 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);(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)(19,586)(20,585)(21,584)(22,583)(23,582)(24,581)(25,580)(26,579)(27,578)(28,577)(29,576)(30,575)(31,574)(32,573)(33,572)(34,571)(35,570)(36,569)(37,568)(38,567)(39,566)(40,565)(41,564)(42,563)(43,562)(44,561)(45,560)(46,559)(47,558)(48,557)(49,556)(50,555)(51,554)(52,553)(53,552)(54,551)(55,550)(56,549)(57,548)(58,547)(59,546)(60,545)(61,544)(62,543)(63,542)(64,541)(65,540)(66,539)(67,538)(68,537)(69,536)(70,535)(71,534)(72,533)(73,532)(74,531)(75,530)(76,529)(77,528)(78,527)(79,526)(80,525)(81,524)(82,523)(83,522)(84,521)(85,520)(86,519)(87,518)(88,517)(89,516)(90,515)(91,514)(92,513)(93,512)(94,511)(95,510)(96,509)(97,508)(98,507)(99,506)(100,505)(101,504)(102,503)(103,502)(104,501)(105,500)(106,499)(107,498)(108,497)(109,496)(110,495)(111,494)(112,493)(113,492)(114,491)(115,490)(116,489)(117,488)(118,487)(119,486)(120,485)(121,484)(122,483)(123,482)(124,481)(125,480)(126,479)(127,478)(128,477)(129,476)(130,475)(131,474)(132,473)(133,472)(134,471)(135,470)(136,469)(137,468)(138,467)(139,466)(140,465)(141,464)(142,463)(143,462)(144,461)(145,460)(146,459)(147,458)(148,457)(149,456)(150,455)(151,454)(152,453)(153,452)(154,451)(155,450)(156,449)(157,448)(158,447)(159,446)(160,445)(161,444)(162,443)(163,442)(164,441)(165,440)(166,439)(167,438)(168,437)(169,436)(170,435)(171,434)(172,433)(173,432)(174,431)(175,430)(176,429)(177,428)(178,427)(179,426)(180,425)(181,424)(182,423)(183,422)(184,421)(185,420)(186,419)(187,418)(188,417)(189,416)(190,415)(191,414)(192,413)(193,412)(194,411)(195,410)(196,409)(197,408)(198,407)(199,406)(200,405)(201,404)(202,403)(203,402)(204,401)(205,400)(206,399)(207,398)(208,397)(209,396)(210,395)(211,394)(212,393)(213,392)(214,391)(215,390)(216,389)(217,388)(218,387)(219,386)(220,385)(221,384)(222,383)(223,382)(224,381)(225,380)(226,379)(227,378)(228,377)(229,376)(230,375)(231,374)(232,373)(233,372)(234,371)(235,370)(236,369)(237,368)(238,367)(239,366)(240,365)(241,364)(242,363)(243,362)(244,361)(245,360)(246,359)(247,358)(248,357)(249,356)(250,355)(251,354)(252,353)(253,352)(254,351)(255,350)(256,349)(257,348)(258,347)(259,346)(260,345)(261,344)(262,343)(263,342)(264,341)(265,340)(266,339)(267,338)(268,337)(269,336)(270,335)(271,334)(272,333)(273,332)(274,331)(275,330)(276,329)(277,328)(278,327)(279,326)(280,325)(281,324)(282,323)(283,322)(284,321)(285,320)(286,319)(287,318)(288,317)(289,316)(290,315)(291,314)(292,313)(293,312)(294,311)(295,310)(296,309)(297,308)(298,307)(299,306)(300,305)(301,304)(302,303)

Polycyclic presentation:

2,17,569|b^a=b^16,c^a=c^568

Conjugacy classes & character table

4838 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19346, 3);

D9673 #34083997