C₂×D₄₁₆₅ #30659397

order	16660
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₈₃₃₀
direct product	C₂×D₄₁₆₅
unambiguous semidirect product	(C₂×C₅)⋊D₈₃₃
unambiguous semidirect product	(C₂×C₁₇)⋊D₂₄₅
unambiguous semidirect product	(C₂×C₄₉)⋊D₈₅

Splittings

Fitting	C₂×C₅×C₁₇×C₄₉ ⋊ C₂
derived, Hall	C₅×C₁₇×C₄₉ ⋊ C₂²
Hall	C₁₇×C₄₉ ⋊ C₂×D₅
Hall	C₅×C₄₉ ⋊ C₂×D₁₇
Hall	C₅×C₁₇ ⋊ C₂×D₄₉
Sylow	C₄₉ ⋊ C₂×D₈₅
Sylow	C₁₇ ⋊ C₂×D₂₄₅
Sylow	C₅ ⋊ C₂×D₈₃₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₄₁₆₅
commutator, cosocle, hypocenter	C₅×C₁₇×C₄₉	C₂²
Frattini	C₇	C₂×D₅₉₅
Fitting	C₂×C₅×C₁₇×C₄₉	C₂
socle	C₂×C₅×C₇×C₁₇	D₇
LCS	G ▷ C₅×C₁₇×C₄₉
UCS	C₁ ◁ C₂

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 8330

A minimal faithful permutation representation — 2 generators on 73 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);(4,7)(5,6)(9,56)(10,55)(11,54)(12,53)(13,52)(14,51)(15,50)(16,49)(17,48)(18,47)(19,46)(20,45)(21,44)(22,43)(23,42)(24,41)(25,40)(26,39)(27,38)(28,37)(29,36)(30,35)(31,34)(32,33)(58,73)(59,72)(60,71)(61,70)(62,69)(63,68)(64,67)(65,66)

Conjugacy classes & character table

4168 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₁₆₆₆₀
maximal normal subgroup of	D₁₆₆₆₀
maximal quotient of	Dic₈₃₃₀, D₁₆₆₆₀

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16660, 29);

C2×D4165 #30659397