D₁₇₆₁₃ #47976326

order	35226
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₇₆₁₃
unambiguous semidirect product	C₉⋊D₁₉₅₇
unambiguous semidirect product	C₁₉⋊D₉₂₇
unambiguous semidirect product	C₁₀₃⋊D₁₇₁

Splittings

Fitting, derived, Hall	C₉×C₁₉×C₁₀₃ ⋊ C₂
Hall	C₁₉×C₁₀₃ ⋊ D₉
Hall	C₉×C₁₀₃ ⋊ D₁₉
Hall	C₉×C₁₉ ⋊ D₁₀₃
Sylow	C₁₀₃ ⋊ D₁₇₁
Sylow	C₁₉ ⋊ D₉₂₇
Sylow	C₉ ⋊ D₁₉₅₇

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₉×C₁₀₃	C₂
Frattini	C₃	D₅₈₇₁
socle	C₃×C₁₉×C₁₀₃	D₃
LCS	G ▷ C₉×C₁₉×C₁₀₃
UCS	C₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 131
transitive degree	μ_t(G) = 17613

A minimal faithful permutation representation — 2 generators on 131 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);(2,9)(3,8)(4,7)(5,6)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)(30,131)(31,130)(32,129)(33,128)(34,127)(35,126)(36,125)(37,124)(38,123)(39,122)(40,121)(41,120)(42,119)(43,118)(44,117)(45,116)(46,115)(47,114)(48,113)(49,112)(50,111)(51,110)(52,109)(53,108)(54,107)(55,106)(56,105)(57,104)(58,103)(59,102)(60,101)(61,100)(62,99)(63,98)(64,97)(65,96)(66,95)(67,94)(68,93)(69,92)(70,91)(71,90)(72,89)(73,88)(74,87)(75,86)(76,85)(77,84)(78,83)(79,82)(80,81)

Polycyclic presentation:

2,3,19,103,3|b^3=e^2,b^a=b^2e,c^a=c^18,d^a=d^102,e^a=e^2

Conjugacy classes & character table

8808 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35226, 12);

D17613 #47976326