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C₄×C₅×Dic₅ #87789

order	400
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₄²×C₅ · Schur multiplier (H₂) = C₄

Aliases

C₄×C₅×Dic₅

Splittings

derived	C₅ ⋊ C₄²×C₅
Sylow	C₅² ⋊ C₄²

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄×C₅	D₅
commutator, hypocenter	C₅	C₄²×C₅
Frattini	C₂²	C₂×C₅×D₅
Fitting	C₂×C₄×C₅²	C₂
socle, prime radical	C₂²×C₅²	C₂²
cosocle	C₂²×C₅	C₂²×C₅
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₄×C₅

76 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)(7,8)(9,10)(15,16,17,18);(6,7,9,10,8)(11,12,13,14)

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	Dic₅×#168, #11716595, #11716610, …
maximal normal subgroup of	Dic₅×#168, #11716595, #11716610, …
maximal quotient of	C₄×C₅×#168, C₅×#3935, C₅×C₈×Dic₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 83);