D₁₇₄₅₉ #46853698

order	34918
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₇₄₅₉
unambiguous semidirect product	C₁₃⋊D₁₃₄₃
unambiguous semidirect product	C₁₇⋊D₁₀₂₇
unambiguous semidirect product	C₇₉⋊D₂₂₁

Splittings

Fitting, socle, derived, Hall	C₁₃×C₁₇×C₇₉ ⋊ C₂
Hall	C₁₇×C₇₉ ⋊ D₁₃
Hall	C₁₃×C₇₉ ⋊ D₁₇
Hall	C₁₃×C₁₇ ⋊ D₇₉
Sylow	C₇₉ ⋊ D₂₂₁
Sylow	C₁₇ ⋊ D₁₀₂₇
Sylow	C₁₃ ⋊ D₁₃₄₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃×C₁₇×C₇₉	C₂
LCS	G ▷ C₁₃×C₁₇×C₇₉
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 109
transitive degree	μ_t(G) = 17459

A minimal faithful permutation representation — 2 generators on 109 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);(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(32,109)(33,108)(34,107)(35,106)(36,105)(37,104)(38,103)(39,102)(40,101)(41,100)(42,99)(43,98)(44,97)(45,96)(46,95)(47,94)(48,93)(49,92)(50,91)(51,90)(52,89)(53,88)(54,87)(55,86)(56,85)(57,84)(58,83)(59,82)(60,81)(61,80)(62,79)(63,78)(64,77)(65,76)(66,75)(67,74)(68,73)(69,72)(70,71)

Polycyclic presentation:

2,13,17,79|b^a=b^12,c^a=c^16,d^a=d^78

Conjugacy classes & character table

8731 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34918, 9);

D17459 #46853698