C₂×D₈₉₉₃ #49112608

order	35972
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₇₉₈₆
direct product	C₂×D₈₉₉₃
unambiguous semidirect product	(C₂×C₁₇)⋊D₅₂₉
unambiguous semidirect product	(C₂×C₅₂₉)⋊D₁₇

Splittings

Fitting	C₂×C₁₇×C₅₂₉ ⋊ C₂
derived, Hall	C₁₇×C₅₂₉ ⋊ C₂²
Sylow	C₅₂₉ ⋊ C₂×D₁₇
Sylow	C₁₇ ⋊ C₂×D₅₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₈₉₉₃
commutator, cosocle, hypocenter	C₁₇×C₅₂₉	C₂²
Frattini	C₂₃	C₂×D₃₉₁
Fitting	C₂×C₁₇×C₅₂₉	C₂
socle	C₂×C₁₇×C₂₃	D₂₃
LCS	G ▷ C₁₇×C₅₂₉
UCS	C₁ ◁ C₂

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 548
transitive degree	μ_t(G) = 17986

A minimal faithful permutation representation — 2 generators on 548 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);(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)(21,548)(22,547)(23,546)(24,545)(25,544)(26,543)(27,542)(28,541)(29,540)(30,539)(31,538)(32,537)(33,536)(34,535)(35,534)(36,533)(37,532)(38,531)(39,530)(40,529)(41,528)(42,527)(43,526)(44,525)(45,524)(46,523)(47,522)(48,521)(49,520)(50,519)(51,518)(52,517)(53,516)(54,515)(55,514)(56,513)(57,512)(58,511)(59,510)(60,509)(61,508)(62,507)(63,506)(64,505)(65,504)(66,503)(67,502)(68,501)(69,500)(70,499)(71,498)(72,497)(73,496)(74,495)(75,494)(76,493)(77,492)(78,491)(79,490)(80,489)(81,488)(82,487)(83,486)(84,485)(85,484)(86,483)(87,482)(88,481)(89,480)(90,479)(91,478)(92,477)(93,476)(94,475)(95,474)(96,473)(97,472)(98,471)(99,470)(100,469)(101,468)(102,467)(103,466)(104,465)(105,464)(106,463)(107,462)(108,461)(109,460)(110,459)(111,458)(112,457)(113,456)(114,455)(115,454)(116,453)(117,452)(118,451)(119,450)(120,449)(121,448)(122,447)(123,446)(124,445)(125,444)(126,443)(127,442)(128,441)(129,440)(130,439)(131,438)(132,437)(133,436)(134,435)(135,434)(136,433)(137,432)(138,431)(139,430)(140,429)(141,428)(142,427)(143,426)(144,425)(145,424)(146,423)(147,422)(148,421)(149,420)(150,419)(151,418)(152,417)(153,416)(154,415)(155,414)(156,413)(157,412)(158,411)(159,410)(160,409)(161,408)(162,407)(163,406)(164,405)(165,404)(166,403)(167,402)(168,401)(169,400)(170,399)(171,398)(172,397)(173,396)(174,395)(175,394)(176,393)(177,392)(178,391)(179,390)(180,389)(181,388)(182,387)(183,386)(184,385)(185,384)(186,383)(187,382)(188,381)(189,380)(190,379)(191,378)(192,377)(193,376)(194,375)(195,374)(196,373)(197,372)(198,371)(199,370)(200,369)(201,368)(202,367)(203,366)(204,365)(205,364)(206,363)(207,362)(208,361)(209,360)(210,359)(211,358)(212,357)(213,356)(214,355)(215,354)(216,353)(217,352)(218,351)(219,350)(220,349)(221,348)(222,347)(223,346)(224,345)(225,344)(226,343)(227,342)(228,341)(229,340)(230,339)(231,338)(232,337)(233,336)(234,335)(235,334)(236,333)(237,332)(238,331)(239,330)(240,329)(241,328)(242,327)(243,326)(244,325)(245,324)(246,323)(247,322)(248,321)(249,320)(250,319)(251,318)(252,317)(253,316)(254,315)(255,314)(256,313)(257,312)(258,311)(259,310)(260,309)(261,308)(262,307)(263,306)(264,305)(265,304)(266,303)(267,302)(268,301)(269,300)(270,299)(271,298)(272,297)(273,296)(274,295)(275,294)(276,293)(277,292)(278,291)(279,290)(280,289)(281,288)(282,287)(283,286)(284,285)

Conjugacy classes & character table

8996 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35972, 11);

C2×D8993 #49112608