Finite Group Databasebeta

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D₃×#23907 #72255263

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹¹

Aliases

Splittings

Fitting	C₃×#23907 ⋊ C₂
Sylow	C₃ ⋊ C₂×#23907

Subgroups

	subgroup	G/H
center	C₂²	C₂×D₃×#120
commutator, cosocle	C₂²×C₃×C₄	C₂⁵
Frattini	C₂²×C₄	C₂⁴×D₃
Fitting	C₃×#23907	C₂
socle	C₂²×C₃	C₂²×#120
prime radical	D₃×#3484	C₂
hypercenter	#23907	D₃
hypocenter	C₃	C₂×#23907
LCS	G ▷ C₂²×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #23907

14140 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×#144415, D₃×#139777, D₃×#139779, …
maximal normal subgroup of	D₃×#144415, D₃×#139777, D₃×#139779, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.