D₁₂₄₅₃ #38735323

order	24906
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₂₄₅₃
unambiguous semidirect product	C₃⋊D₄₁₅₁
unambiguous semidirect product	C₇⋊D₁₇₇₉
unambiguous semidirect product	C₅₉₃⋊D₂₁

Splittings

Fitting, socle, derived, Hall	C₃×C₇×C₅₉₃ ⋊ C₂
Hall	C₇×C₅₉₃ ⋊ D₃
Hall	C₃×C₅₉₃ ⋊ D₇
Sylow	C₅₉₃ ⋊ D₂₁
Hall	C₃×C₇ ⋊ D₅₉₃
Sylow	C₇ ⋊ D₁₇₇₉
Sylow	C₃ ⋊ D₄₁₅₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₅₉₃	C₂
LCS	G ▷ C₃×C₇×C₅₉₃
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 603
transitive degree	μ_t(G) = 12453

A minimal faithful permutation representation — 2 generators on 603 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);(2,3)(5,10)(6,9)(7,8)(12,603)(13,602)(14,601)(15,600)(16,599)(17,598)(18,597)(19,596)(20,595)(21,594)(22,593)(23,592)(24,591)(25,590)(26,589)(27,588)(28,587)(29,586)(30,585)(31,584)(32,583)(33,582)(34,581)(35,580)(36,579)(37,578)(38,577)(39,576)(40,575)(41,574)(42,573)(43,572)(44,571)(45,570)(46,569)(47,568)(48,567)(49,566)(50,565)(51,564)(52,563)(53,562)(54,561)(55,560)(56,559)(57,558)(58,557)(59,556)(60,555)(61,554)(62,553)(63,552)(64,551)(65,550)(66,549)(67,548)(68,547)(69,546)(70,545)(71,544)(72,543)(73,542)(74,541)(75,540)(76,539)(77,538)(78,537)(79,536)(80,535)(81,534)(82,533)(83,532)(84,531)(85,530)(86,529)(87,528)(88,527)(89,526)(90,525)(91,524)(92,523)(93,522)(94,521)(95,520)(96,519)(97,518)(98,517)(99,516)(100,515)(101,514)(102,513)(103,512)(104,511)(105,510)(106,509)(107,508)(108,507)(109,506)(110,505)(111,504)(112,503)(113,502)(114,501)(115,500)(116,499)(117,498)(118,497)(119,496)(120,495)(121,494)(122,493)(123,492)(124,491)(125,490)(126,489)(127,488)(128,487)(129,486)(130,485)(131,484)(132,483)(133,482)(134,481)(135,480)(136,479)(137,478)(138,477)(139,476)(140,475)(141,474)(142,473)(143,472)(144,471)(145,470)(146,469)(147,468)(148,467)(149,466)(150,465)(151,464)(152,463)(153,462)(154,461)(155,460)(156,459)(157,458)(158,457)(159,456)(160,455)(161,454)(162,453)(163,452)(164,451)(165,450)(166,449)(167,448)(168,447)(169,446)(170,445)(171,444)(172,443)(173,442)(174,441)(175,440)(176,439)(177,438)(178,437)(179,436)(180,435)(181,434)(182,433)(183,432)(184,431)(185,430)(186,429)(187,428)(188,427)(189,426)(190,425)(191,424)(192,423)(193,422)(194,421)(195,420)(196,419)(197,418)(198,417)(199,416)(200,415)(201,414)(202,413)(203,412)(204,411)(205,410)(206,409)(207,408)(208,407)(209,406)(210,405)(211,404)(212,403)(213,402)(214,401)(215,400)(216,399)(217,398)(218,397)(219,396)(220,395)(221,394)(222,393)(223,392)(224,391)(225,390)(226,389)(227,388)(228,387)(229,386)(230,385)(231,384)(232,383)(233,382)(234,381)(235,380)(236,379)(237,378)(238,377)(239,376)(240,375)(241,374)(242,373)(243,372)(244,371)(245,370)(246,369)(247,368)(248,367)(249,366)(250,365)(251,364)(252,363)(253,362)(254,361)(255,360)(256,359)(257,358)(258,357)(259,356)(260,355)(261,354)(262,353)(263,352)(264,351)(265,350)(266,349)(267,348)(268,347)(269,346)(270,345)(271,344)(272,343)(273,342)(274,341)(275,340)(276,339)(277,338)(278,337)(279,336)(280,335)(281,334)(282,333)(283,332)(284,331)(285,330)(286,329)(287,328)(288,327)(289,326)(290,325)(291,324)(292,323)(293,322)(294,321)(295,320)(296,319)(297,318)(298,317)(299,316)(300,315)(301,314)(302,313)(303,312)(304,311)(305,310)(306,309)(307,308)

Polycyclic presentation:

2,3,7,593|b^a=b^2,c^a=c^6,d^a=d^592

Conjugacy classes & character table

6228 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24906, 9);

D12453 #38735323