D₁₇₆₆₇ #47977461

order	35334
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₇₆₆₇
unambiguous semidirect product	C₉⋊D₁₉₆₃
unambiguous semidirect product	C₁₃⋊D₁₃₅₉
unambiguous semidirect product	C₁₅₁⋊D₁₁₇

Splittings

Fitting, derived, Hall	C₉×C₁₃×C₁₅₁ ⋊ C₂
Hall	C₁₃×C₁₅₁ ⋊ D₉
Hall	C₉×C₁₅₁ ⋊ D₁₃
Sylow	C₁₅₁ ⋊ D₁₁₇
Hall	C₉×C₁₃ ⋊ D₁₅₁
Sylow	C₁₃ ⋊ D₁₃₅₉
Sylow	C₉ ⋊ D₁₉₆₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₃×C₁₅₁	C₂
Frattini	C₃	D₅₈₈₉
socle	C₃×C₁₃×C₁₅₁	D₃
LCS	G ▷ C₉×C₁₃×C₁₅₁
UCS	C₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 173
transitive degree	μ_t(G) = 17667

A minimal faithful permutation representation — 2 generators on 173 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);(2,9)(3,8)(4,7)(5,6)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(24,173)(25,172)(26,171)(27,170)(28,169)(29,168)(30,167)(31,166)(32,165)(33,164)(34,163)(35,162)(36,161)(37,160)(38,159)(39,158)(40,157)(41,156)(42,155)(43,154)(44,153)(45,152)(46,151)(47,150)(48,149)(49,148)(50,147)(51,146)(52,145)(53,144)(54,143)(55,142)(56,141)(57,140)(58,139)(59,138)(60,137)(61,136)(62,135)(63,134)(64,133)(65,132)(66,131)(67,130)(68,129)(69,128)(70,127)(71,126)(72,125)(73,124)(74,123)(75,122)(76,121)(77,120)(78,119)(79,118)(80,117)(81,116)(82,115)(83,114)(84,113)(85,112)(86,111)(87,110)(88,109)(89,108)(90,107)(91,106)(92,105)(93,104)(94,103)(95,102)(96,101)(97,100)(98,99)

Polycyclic presentation:

2,3,13,151,3|b^3=e^2,b^a=b^2e,c^a=c^12,d^a=d^150,e^a=e^2

Conjugacy classes & character table

8835 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35334, 12);

D17667 #47977461