D₁₅₅₁₇ #44526743

order	31034
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₅₅₁₇
unambiguous semidirect product	C₅₉⋊D₂₆₃
unambiguous semidirect product	C₂₆₃⋊D₅₉

Splittings

Fitting, socle, derived, Hall	C₅₉×C₂₆₃ ⋊ C₂
Sylow	C₂₆₃ ⋊ D₅₉
Sylow	C₅₉ ⋊ D₂₆₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅₉×C₂₆₃	C₂
LCS	G ▷ C₅₉×C₂₆₃
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 322
transitive degree	μ_t(G) = 15517

A minimal faithful permutation representation — 2 generators on 322 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);(2,59)(3,58)(4,57)(5,56)(6,55)(7,54)(8,53)(9,52)(10,51)(11,50)(12,49)(13,48)(14,47)(15,46)(16,45)(17,44)(18,43)(19,42)(20,41)(21,40)(22,39)(23,38)(24,37)(25,36)(26,35)(27,34)(28,33)(29,32)(30,31)(61,322)(62,321)(63,320)(64,319)(65,318)(66,317)(67,316)(68,315)(69,314)(70,313)(71,312)(72,311)(73,310)(74,309)(75,308)(76,307)(77,306)(78,305)(79,304)(80,303)(81,302)(82,301)(83,300)(84,299)(85,298)(86,297)(87,296)(88,295)(89,294)(90,293)(91,292)(92,291)(93,290)(94,289)(95,288)(96,287)(97,286)(98,285)(99,284)(100,283)(101,282)(102,281)(103,280)(104,279)(105,278)(106,277)(107,276)(108,275)(109,274)(110,273)(111,272)(112,271)(113,270)(114,269)(115,268)(116,267)(117,266)(118,265)(119,264)(120,263)(121,262)(122,261)(123,260)(124,259)(125,258)(126,257)(127,256)(128,255)(129,254)(130,253)(131,252)(132,251)(133,250)(134,249)(135,248)(136,247)(137,246)(138,245)(139,244)(140,243)(141,242)(142,241)(143,240)(144,239)(145,238)(146,237)(147,236)(148,235)(149,234)(150,233)(151,232)(152,231)(153,230)(154,229)(155,228)(156,227)(157,226)(158,225)(159,224)(160,223)(161,222)(162,221)(163,220)(164,219)(165,218)(166,217)(167,216)(168,215)(169,214)(170,213)(171,212)(172,211)(173,210)(174,209)(175,208)(176,207)(177,206)(178,205)(179,204)(180,203)(181,202)(182,201)(183,200)(184,199)(185,198)(186,197)(187,196)(188,195)(189,194)(190,193)(191,192)

Polycyclic presentation:

2,59,263|b^a=b^58,c^a=c^262

Conjugacy classes & character table

7760 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₅₅₁₇
maximal normal subgroup of	C₂×D₁₅₅₁₇
maximal quotient of	Dic₁₅₅₁₇, C₂×D₁₅₅₁₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31034, 3);

D15517 #44526743