Finite Group Databasebeta

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C₂×C₄²×D₅⋊AGL(1,𝔽₅) #72269253

order	6400
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄³ · Schur multiplier (H₂) = C₂⁷×C₄³

Aliases

C₂×C₄²×D₅⋊AGL(1,𝔽₅)

Splittings

Fitting	C₂×C₄²×C₅² ⋊ C₂×C₄
derived, Sylow	C₅² ⋊ C₂²×C₄³

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄²	D₅⋊AGL(1,𝔽₅)
commutator, hypocenter	C₅²	C₂²×C₄³
Frattini	C₂²	C₂³×D₅⋊AGL(1,𝔽₅)
Fitting	C₂×C₄²×C₅²	C₂×C₄
socle	C₂³×C₅²	C₂³×C₄
prime radical	C₂³×D₅²	C₂³
cosocle	C₂²×C₅⋊D₅	C₂⁵
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₄²

17460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 320

Conjugacy classes & character table

448 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.