Finite Group Databasebeta

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C₄²×C₃⋊D₃×AGL(1,𝔽₅) #72231544

order	5760
automorphism	?
homology	Abelianization (H₁) = C₂×C₄³ · Schur multiplier (H₂) = C₂³×C₃×C₄³

Aliases

C₄²×C₃⋊D₃×AGL(1,𝔽₅)

Splittings

Fitting	C₃²×C₄²×C₅ ⋊ C₂×C₄
derived, Hall	C₃²×C₅ ⋊ C₂×C₄³
Sylow	C₃² ⋊ C₂×C₄²×AGL(1,𝔽₅)
Sylow	C₅ ⋊ C₄³×C₃⋊D₃

Subgroups

	subgroup	G/H
center, hypercenter	C₄²	C₃⋊D₃×AGL(1,𝔽₅)
commutator, hypocenter	C₃²×C₅	C₂×C₄³
Frattini	C₂²	C₂²×C₃⋊D₃×AGL(1,𝔽₅)
Fitting	C₃²×C₄²×C₅	C₂×C₄
socle	C₂²×C₃²×C₅	C₂³×C₄
prime radical	C₂²×D₅×C₃⋊D₃	C₂³
cosocle	C₂²×C₃²×D₅	C₂⁴
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₄²

7632 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 720

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃⋊D₃×AGL(1,𝔽₅)×#127
maximal normal subgroup of	C₃⋊D₃×AGL(1,𝔽₅)×#127

GAP

Past the SmallGroups library coverage — no SmallGroups id.