Finite Group Databasebeta

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D₃×#20609 #72248154

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹³

Aliases

Splittings

Fitting	C₃×#20609 ⋊ C₂
Sylow	C₃ ⋊ C₂×#20609

Subgroups

	subgroup	G/H
center	C₂²	C₂×D₃×#120
commutator	C₂³×C₃	C₂⁴×C₄
Frattini	C₂⁴	C₂⁴×D₃
Fitting	C₃×#20609	C₂
socle	C₂²×C₃	C₂²×#120
prime radical	C₂²×D₃×H(5,𝔽₂)	C₂
cosocle	C₂⁴×C₃	C₂⁵
hypercenter	#20609	D₃
hypocenter	C₃	C₂×#20609
LCS	G ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ #20609

38044 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#394064, D₃×#494600, D₃×#498927, …
maximal normal subgroup of	D₃×#394064, D₃×#494600, D₃×#498927, …
maximal quotient of	D₃×#187928, D₃×#493635

GAP

Past the SmallGroups library coverage — no SmallGroups id.