Finite Group Databasebeta

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D₃×#34406 #72248306

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₄ · Schur multiplier (H₂) = C₂¹³

Aliases

Splittings

Fitting	C₃×#34406 ⋊ C₂
Sylow	C₃ ⋊ C₂×#34406

Subgroups

	subgroup	G/H
center, Frattini	C₂³	C₂⁵×D₃
commutator	C₂²×C₃	C₂⁵×C₄
Fitting	C₃×#34406	C₂
socle, cosocle	C₂³×C₃	C₂⁶
prime radical	C₂×D₃×#535	C₂
hypercenter	#34406	D₃
hypocenter	C₃	C₂×#34406
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ #34406

21268 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 192

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#146654, D₃×#494600, D₃×#7792761
maximal normal subgroup of	D₃×#146654, D₃×#494600, D₃×#7792761
maximal quotient of	D₃×#581603

GAP

Past the SmallGroups library coverage — no SmallGroups id.