Finite Group Databasebeta

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D₃×#23573 #72269954

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹⁰

Aliases

Splittings

Fitting	C₃×#23573 ⋊ C₂
Sylow	C₃ ⋊ C₂×#23573

Subgroups

	subgroup	G/H
center	C₂³	C₂²×D₃×D₄
commutator, cosocle	C₂²×C₃×C₄	C₂⁵
Frattini	C₂²×C₄	C₂⁴×D₃
Fitting	C₃×#23573	C₂
socle	C₂³×C₃	C₂³×D₄
hypercenter	#23573	D₃
hypocenter	C₃	C₂×#23573
LCS	G ▷ C₂²×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #23573

10308 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 384

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#6453969
maximal normal subgroup of	D₃×#6453969
maximal quotient of	D₃×#499269

GAP

Past the SmallGroups library coverage — no SmallGroups id.