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C₅×Dic₂₀ #87786

order	400
isoclinism	isoclinic class of #677
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₁

Aliases

C₅×Dic₂₀

Splittings

C₅² ⋊ Q₁₆

Subgroups

	subgroup	G/H
center	C₂×C₅	D₂₀
commutator, cosocle	C₄×C₅	C₂²×C₅
Frattini	C₄	C₂×C₅×D₅
Fitting	C₅²×C₈	C₂
socle, prime radical	C₂×C₅²	D₄
hypercenter	C₅×C₈	D₅
hypocenter	C₅	C₅×Q₁₆
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×C₈

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 80

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2,3,4,5)(6,7,9,10,8)(11,22,20,21,15,13,14,24)(12,25,23,19,18,16,17,26);(7,8)(9,10)(11,12,15,18)(13,19,22,26)(14,23,20,17)(16,24,25,21)

Conjugacy classes & character table

115 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11716588, #11716590, #11716591, …
maximal normal subgroup of	#11716588, #11716590, #11716591, …
maximal quotient of	C₅×#3948, C₅×#3950, C₂×C₅×Dic₂₀, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 80);