Finite Group Databasebeta

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D₃×#11004 #72248740

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

Splittings

Fitting	C₃×#11004 ⋊ C₂
Sylow	C₃ ⋊ C₂×#11004

Subgroups

	subgroup	G/H
center	C₂²	D₃×#392
commutator	C₂²×C₃×C₄	C₂³×C₄
Frattini	C₂³×C₄	C₂³×D₃
Fitting	C₃×#11004	C₂
socle	C₂²×C₃	C₂×#392
prime radical	C₂×D₃×#535	C₂
cosocle	C₂³×C₃×C₄	C₂⁴
hypercenter	#11004	D₃
hypocenter	C₃	C₂×#11004
LCS	G ▷ C₂²×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #11004

10252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#417670, D₃×#394102, D₃×#394321, …
maximal normal subgroup of	D₃×#417670, D₃×#394102, D₃×#394321, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.