D₈₈₄₅ #31799115

order	17690
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₈₈₄₅
unambiguous semidirect product	C₅⋊D₁₇₆₉
unambiguous semidirect product	C₂₉⋊D₃₀₅
unambiguous semidirect product	C₆₁⋊D₁₄₅

Splittings

Fitting, socle, derived, Hall	C₅×C₂₉×C₆₁ ⋊ C₂
Hall	C₂₉×C₆₁ ⋊ D₅
Hall	C₅×C₆₁ ⋊ D₂₉
Hall	C₅×C₂₉ ⋊ D₆₁
Sylow	C₆₁ ⋊ D₁₄₅
Sylow	C₂₉ ⋊ D₃₀₅
Sylow	C₅ ⋊ D₁₇₆₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₂₉×C₆₁	C₂
LCS	G ▷ C₅×C₂₉×C₆₁
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 95
transitive degree	μ_t(G) = 8845

A minimal faithful permutation representation — 2 generators on 95 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);(2,5)(3,4)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)(36,95)(37,94)(38,93)(39,92)(40,91)(41,90)(42,89)(43,88)(44,87)(45,86)(46,85)(47,84)(48,83)(49,82)(50,81)(51,80)(52,79)(53,78)(54,77)(55,76)(56,75)(57,74)(58,73)(59,72)(60,71)(61,70)(62,69)(63,68)(64,67)(65,66)

Polycyclic presentation:

2,5,29,61|b^a=b^4,c^a=c^28,d^a=d^60

Conjugacy classes & character table

4424 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	#47978077, #47978078, #47978081, …
maximal normal subgroup of	#47978077, #47978078, #47978081, …
maximal quotient of	Dic₈₈₄₅, C₂×D₈₈₄₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17690, 9);

D8845 #31799115