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C₅×D₄×D₅ #87891

order	400
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂³

Aliases

C₅×D₄×D₅

Splittings

Fitting	C₅²×D₄ ⋊ C₂
Sylow	C₅² ⋊ C₂×D₄

Subgroups

	subgroup	G/H
center	C₂×C₅	C₂²×D₅
commutator, cosocle	C₂×C₅	C₂³×C₅
Frattini	C₂	C₂²×C₅×D₅
Fitting	C₅²×D₄	C₂
socle	C₂×C₅²	C₂³
hypercenter	C₅×D₄	D₅
hypocenter	C₅	C₂×C₅×D₄
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₅ ◁ C₅×D₄

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)(7,8)(9,10);(6,7,9,10,8)(12,14);(11,12)(13,14)

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×#4007, #11716850, D₅×#686, …
maximal normal subgroup of	C₅×#4007, #11716850, D₅×#686, …
maximal quotient of	C₅×#4024, C₅×D₅×C₂²⋊C₄, C₅×#4027, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 185);