Dic₇₈₇₁ #44538412

order	31484
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₇₈₇₁
unambiguous semidirect product	C₄₆₃⋊Dic₁₇

Splittings

derived, Hall	C₁₇×C₄₆₃ ⋊ C₄
Sylow	C₄₆₃ ⋊ Dic₁₇
Sylow	C₁₇ ⋊ Dic₄₆₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₇₈₇₁
commutator, hypocenter	C₁₇×C₄₆₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₁₇×C₄₆₃	C₂
LCS	G ▷ C₁₇×C₄₆₃
UCS	C₁ ◁ C₂

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 484
transitive degree	μ_t(G) = 31484

A minimal faithful permutation representation — 2 generators on 484 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);(1,3,2,4)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)(23,484)(24,483)(25,482)(26,481)(27,480)(28,479)(29,478)(30,477)(31,476)(32,475)(33,474)(34,473)(35,472)(36,471)(37,470)(38,469)(39,468)(40,467)(41,466)(42,465)(43,464)(44,463)(45,462)(46,461)(47,460)(48,459)(49,458)(50,457)(51,456)(52,455)(53,454)(54,453)(55,452)(56,451)(57,450)(58,449)(59,448)(60,447)(61,446)(62,445)(63,444)(64,443)(65,442)(66,441)(67,440)(68,439)(69,438)(70,437)(71,436)(72,435)(73,434)(74,433)(75,432)(76,431)(77,430)(78,429)(79,428)(80,427)(81,426)(82,425)(83,424)(84,423)(85,422)(86,421)(87,420)(88,419)(89,418)(90,417)(91,416)(92,415)(93,414)(94,413)(95,412)(96,411)(97,410)(98,409)(99,408)(100,407)(101,406)(102,405)(103,404)(104,403)(105,402)(106,401)(107,400)(108,399)(109,398)(110,397)(111,396)(112,395)(113,394)(114,393)(115,392)(116,391)(117,390)(118,389)(119,388)(120,387)(121,386)(122,385)(123,384)(124,383)(125,382)(126,381)(127,380)(128,379)(129,378)(130,377)(131,376)(132,375)(133,374)(134,373)(135,372)(136,371)(137,370)(138,369)(139,368)(140,367)(141,366)(142,365)(143,364)(144,363)(145,362)(146,361)(147,360)(148,359)(149,358)(150,357)(151,356)(152,355)(153,354)(154,353)(155,352)(156,351)(157,350)(158,349)(159,348)(160,347)(161,346)(162,345)(163,344)(164,343)(165,342)(166,341)(167,340)(168,339)(169,338)(170,337)(171,336)(172,335)(173,334)(174,333)(175,332)(176,331)(177,330)(178,329)(179,328)(180,327)(181,326)(182,325)(183,324)(184,323)(185,322)(186,321)(187,320)(188,319)(189,318)(190,317)(191,316)(192,315)(193,314)(194,313)(195,312)(196,311)(197,310)(198,309)(199,308)(200,307)(201,306)(202,305)(203,304)(204,303)(205,302)(206,301)(207,300)(208,299)(209,298)(210,297)(211,296)(212,295)(213,294)(214,293)(215,292)(216,291)(217,290)(218,289)(219,288)(220,287)(221,286)(222,285)(223,284)(224,283)(225,282)(226,281)(227,280)(228,279)(229,278)(230,277)(231,276)(232,275)(233,274)(234,273)(235,272)(236,271)(237,270)(238,269)(239,268)(240,267)(241,266)(242,265)(243,264)(244,263)(245,262)(246,261)(247,260)(248,259)(249,258)(250,257)(251,256)(252,255)(253,254)

Polycyclic presentation:

2,17,463,2|a^2=d,b^a=b^16,c^a=c^462

Conjugacy classes & character table

7874 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	Dic₁₅₇₄₂
maximal normal subgroup of	Dic₁₅₇₄₂

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31484, 4);

Dic7871 #44538412