Finite Group Databasebeta

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D₃×#32891 #72270083

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹²

Aliases

Splittings

Fitting	C₃×#32891 ⋊ C₂
Sylow	C₃ ⋊ C₂×#32891

Subgroups

	subgroup	G/H
center	C₂²	C₂×D₃×#120
commutator, cosocle	C₂²×C₃×C₄	C₂⁵
Frattini	C₂²×C₄	C₂⁴×D₃
Fitting	C₃×#32891	C₂
socle	C₂²×C₃	C₂²×#120
prime radical	C₂²×D₃×H(5,𝔽₂)	C₂
hypercenter	#32891	D₃
hypocenter	C₃	C₂×#32891
LCS	G ▷ C₂²×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #32891

36860 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

147 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#6628867
maximal normal subgroup of	D₃×#6628867

GAP

Past the SmallGroups library coverage — no SmallGroups id.