D₁₇₃₂₉ #46831704

order	34658
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₇₃₂₉
unambiguous semidirect product	C₁₃⋊D₁₃₃₃
unambiguous semidirect product	C₃₁⋊D₅₅₉
unambiguous semidirect product	C₄₃⋊D₄₀₃

Splittings

Fitting, socle, derived, Hall	C₁₃×C₃₁×C₄₃ ⋊ C₂
Hall	C₃₁×C₄₃ ⋊ D₁₃
Hall	C₁₃×C₄₃ ⋊ D₃₁
Hall	C₁₃×C₃₁ ⋊ D₄₃
Sylow	C₄₃ ⋊ D₄₀₃
Sylow	C₃₁ ⋊ D₅₅₉
Sylow	C₁₃ ⋊ D₁₃₃₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃×C₃₁×C₄₃	C₂
LCS	G ▷ C₁₃×C₃₁×C₄₃
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 87
transitive degree	μ_t(G) = 17329

A minimal faithful permutation representation — 2 generators on 87 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);(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,44)(16,43)(17,42)(18,41)(19,40)(20,39)(21,38)(22,37)(23,36)(24,35)(25,34)(26,33)(27,32)(28,31)(29,30)(46,87)(47,86)(48,85)(49,84)(50,83)(51,82)(52,81)(53,80)(54,79)(55,78)(56,77)(57,76)(58,75)(59,74)(60,73)(61,72)(62,71)(63,70)(64,69)(65,68)(66,67)

Polycyclic presentation:

2,13,31,43|b^a=b^12,c^a=c^30,d^a=d^42

Conjugacy classes & character table

8666 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34658, 8);

D17329 #46831704