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D₅×D₂₀ #87876

order	400
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

D₅×D₂₀

Splittings

Fitting	C₄×C₅² ⋊ C₂²
Sylow	C₅² ⋊ C₂×D₄

Subgroups

	subgroup	G/H
center, Frattini	C₂	C₂×D₅²
commutator, socle, cosocle	C₂×C₅²	C₂³
Fitting	C₄×C₅²	C₂²
hypercenter	C₄	D₅²
hypocenter	C₅²	C₂×D₄
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂ ◁ C₄

124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 40

A minimal faithful permutation representation — 3 generators on 14 points:

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11716734, #11716735, D₅×#677, …
maximal normal subgroup of	#11716734, #11716735, D₅×#677, …
maximal quotient of	D₅×#677, D₅×D₄₀, #11716912, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 170);