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C₅×D₄₀ #87785

order	400
isoclinism	isoclinic class of #677
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

C₅×D₄₀

Splittings

Fitting	C₅²×C₈ ⋊ C₂
Sylow	C₅² ⋊ D₈

Subgroups

	subgroup	G/H
center	C₂×C₅	D₂₀
commutator, cosocle	C₄×C₅	C₂²×C₅
Frattini	C₄	C₂×C₅×D₅
Fitting	C₅²×C₈	C₂
socle	C₂×C₅²	D₄
hypercenter	C₅×C₈	D₅
hypocenter	C₅	C₅×D₈
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×C₈

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 80

A minimal faithful permutation representation — 2 generators on 18 points:

(1,2,3,4,5)(6,7,9,10,8)(11,17,16,15,14,12,13,18);(7,8)(9,10)(12,15)(13,16)(17,18)

Conjugacy classes & character table

115 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11716586, #11716587, #11716588, …
maximal normal subgroup of	#11716586, #11716587, #11716588, …
maximal quotient of	C₅×D₈₀, C₅×#3932, C₅×Dic₄₀, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 79);