Finite Group Databasebeta

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D₃×C₃⋊D₃×AGL(1,ℤ/8) #72243279

order	3456
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁹×C₃

Aliases

D₃×C₃⋊D₃×AGL(1,ℤ/8)

Splittings

Fitting	C₃³×AGL(1,ℤ/8) ⋊ C₂²
Sylow	C₃³ ⋊ C₂²×AGL(1,ℤ/8)

Subgroups

	subgroup	G/H
center	C₂	C₂×D₃×D₄×C₃⋊D₃
commutator, cosocle	C₃³×C₄	C₂⁵
Frattini	C₄	C₂³×D₃×C₃⋊D₃
Fitting	C₃³×AGL(1,ℤ/8)	C₂²
socle	C₂×C₃³	C₂³×D₄
hypercenter	AGL(1,ℤ/8)	D₃×C₃⋊D₃
hypocenter	C₃³	C₂²×AGL(1,ℤ/8)
LCS	G ▷ C₃³×C₄ ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ AGL(1,ℤ/8)

11512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 144

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

Relationships

maximal quotient of

D₃×C₃⋊D₃×#442

GAP

Past the SmallGroups library coverage — no SmallGroups id.