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D₁₄₀ #63321

order	280
isoclinism	isoclinic class of Dic₇₀
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₄₀
unambiguous semidirect product	C₄⋊D₃₅

Splittings

Fitting	C₄×C₅×C₇ ⋊ C₂
Hall	C₅×C₇ ⋊ D₄
Sylow	C₇ ⋊ D₂₀
Sylow	C₅ ⋊ D₂₈

Subgroups

	subgroup	G/H
center, Frattini	C₂	C₂×D₃₅
commutator, socle, cosocle	C₂×C₅×C₇	C₂²
Fitting	C₄×C₅×C₇	C₂
hypercenter	C₄	D₃₅
hypocenter	C₅×C₇	D₄
LCS	G ▷ C₂×C₅×C₇ ▷ C₅×C₇
UCS	C₁ ◁ C₂ ◁ C₄

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 140

A minimal faithful permutation representation — 2 generators on 16 points:

(1,2,3,4)(5,6,7,8,9)(10,11,12,13,14,15,16);(2,4)(6,9)(7,8)(11,16)(12,15)(13,14)

Polycyclic presentation:

2^3,5,7|b^2=c,b^a=bc,d^a=d^4,e^a=e^6

Conjugacy classes & character table

73 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10587842, #10587843, #10587847, …
maximal normal subgroup of	#10587842, #10587843, #10587847, …
maximal quotient of	#10587894, D₂₈₀, Dic₁₄₀, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(280, 26);