D₉₁₉₇ #32913680

order	18394
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₉₁₉₇
unambiguous semidirect product	C₁₇⋊D₅₄₁
unambiguous semidirect product	C₅₄₁⋊D₁₇

Splittings

Fitting, socle, derived, Hall	C₁₇×C₅₄₁ ⋊ C₂
Sylow	C₅₄₁ ⋊ D₁₇
Sylow	C₁₇ ⋊ D₅₄₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₇×C₅₄₁	C₂
LCS	G ▷ C₁₇×C₅₄₁
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 558
transitive degree	μ_t(G) = 9197

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

Polycyclic presentation:

2,17,541|b^a=b^16,c^a=c^540

Conjugacy classes & character table

4600 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	#49145469, #49145470, D₁₇×D₅₄₁, …
maximal normal subgroup of	#49145469, #49145470, D₁₇×D₅₄₁, …
maximal quotient of	Dic₉₁₉₇, C₂×D₉₁₉₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18394, 3);

D9197 #32913680