Finite Group Databasebeta

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#120×D₅⋊AGL(1,𝔽₅) #72222309

order	6400
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹¹

Aliases

#120×D₅⋊AGL(1,𝔽₅)

Splittings

Fitting	C₅²×#120 ⋊ C₂×C₄
Sylow	C₅² ⋊ C₂×C₄×#120

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₅⋊AGL(1,𝔽₅)
commutator, socle	C₂²×C₅²	C₂⁴×C₄
Fitting	C₅²×#120	C₂×C₄
prime radical	D₅²×#120	C₂
cosocle	C₂²×C₅⋊D₅	C₂⁵
hypercenter	#120	D₅⋊AGL(1,𝔽₅)
hypocenter	C₅²	C₂×C₄×#120
LCS	G ▷ C₂²×C₅² ▷ C₅²
UCS	C₁ ◁ C₂² ◁ #120

18388 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

Relationships

maximal subgroup of

#1020×D₅⋊AGL(1,𝔽₅)

GAP

Past the SmallGroups library coverage — no SmallGroups id.