C₂×D₄₀₀₅ #30630825

order	16020
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₈₀₁₀
direct product	C₂×D₄₀₀₅
unambiguous semidirect product	(C₂×C₅)⋊D₈₀₁
unambiguous semidirect product	(C₂×C₉)⋊D₄₄₅
unambiguous semidirect product	(C₂×C₈₉)⋊D₄₅

Splittings

Fitting	C₂×C₅×C₉×C₈₉ ⋊ C₂
derived, Hall	C₅×C₉×C₈₉ ⋊ C₂²
Hall	C₉×C₈₉ ⋊ C₂×D₅
Hall	C₅×C₈₉ ⋊ C₂×D₉
Sylow	C₈₉ ⋊ C₂×D₄₅
Hall	C₅×C₉ ⋊ C₂×D₈₉
Sylow	C₉ ⋊ C₂×D₄₄₅
Sylow	C₅ ⋊ C₂×D₈₀₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₄₀₀₅
commutator, cosocle, hypocenter	C₅×C₉×C₈₉	C₂²
Frattini	C₃	C₂×D₁₃₃₅
Fitting	C₂×C₅×C₉×C₈₉	C₂
socle	C₂×C₃×C₅×C₈₉	D₃
LCS	G ▷ C₅×C₉×C₈₉
UCS	C₁ ◁ C₂

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 105
transitive degree	μ_t(G) = 8010

A minimal faithful permutation representation — 2 generators on 105 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);(4,11)(5,10)(6,9)(7,8)(13,16)(14,15)(18,105)(19,104)(20,103)(21,102)(22,101)(23,100)(24,99)(25,98)(26,97)(27,96)(28,95)(29,94)(30,93)(31,92)(32,91)(33,90)(34,89)(35,88)(36,87)(37,86)(38,85)(39,84)(40,83)(41,82)(42,81)(43,80)(44,79)(45,78)(46,77)(47,76)(48,75)(49,74)(50,73)(51,72)(52,71)(53,70)(54,69)(55,68)(56,67)(57,66)(58,65)(59,64)(60,63)(61,62)

Conjugacy classes & character table

4008 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₁₆₀₂₀, C₂×D₁₂₀₁₅
maximal normal subgroup of	D₁₆₀₂₀
maximal quotient of	Dic₈₀₁₀, D₁₆₀₂₀, C₂×D₁₂₀₁₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16020, 30);

C2×D4005 #30630825