Finite Group Databasebeta

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C₃×AGL(1,𝔽₅)×D₅⋊AGL(1,𝔽₅) #72269187

order	12000
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄² · Schur multiplier (H₂) = C₂²×C₄

Aliases

C₃×AGL(1,𝔽₅)×D₅⋊AGL(1,𝔽₅)

Splittings

Fitting, socle, Hall	C₃×C₅³ ⋊ C₂×C₄²
derived, Sylow	C₅³ ⋊ C₂×C₃×C₄²

Subgroups

	subgroup	G/H
center, hypercenter	C₃	AGL(1,𝔽₅)×D₅⋊AGL(1,𝔽₅)
commutator, hypocenter	C₅³	C₂×C₃×C₄²
Frattini	C₁	G
Fitting, socle	C₃×C₅³	C₂×C₄²
prime radical	C₃×D₅³	C₂²
cosocle	D₅×C₅⋊D₅	C₂³×C₃
LCS	G ▷ C₅³
UCS	C₁ ◁ C₃

1072 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 120

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.