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C₂×C₄⋊(C₅⋊D₅) #87899

order	400
isoclinism	isoclinic class of #6045
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³×C₅

Aliases

C₂×C₄⋊(C₅⋊D₅)

Splittings

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

Subgroups

	subgroup	G/H
center	C₂²	C₂×C₅⋊D₅
commutator, cosocle	C₂×C₅²	C₂³
Frattini	C₂	C₂²×C₅⋊D₅
Fitting	C₂×C₄×C₅²	C₂
socle	C₂²×C₅²	C₂²
hypercenter	C₂×C₄	C₅⋊D₅
hypocenter	C₅²	C₂×D₄
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂² ◁ C₂×C₄

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 200

A minimal faithful permutation representation — 3 generators on 16 points:

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

Conjugacy classes & character table

106 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11716600, #11716605, #11716676, …
maximal normal subgroup of	#11716600, #11716605, #11716676, …
maximal quotient of	#11717189, C₄×C₄⋊(C₅⋊D₅), #11717194, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 193);