Finite Group Databasebeta

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D₃×#23984 #72271140

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

Aliases

Splittings

Fitting	C₃×#23984 ⋊ C₂
Sylow	C₃ ⋊ C₂×#23984

Subgroups

	subgroup	G/H
center	C₂²	C₂×D₃×#120
commutator, cosocle	C₂⁴×C₃	C₂⁵
Frattini	C₂⁴	C₂⁴×D₃
Fitting	C₃×#23984	C₂
socle	C₂²×C₃	C₂²×#120
hypercenter	#23984	D₃
hypocenter	C₃	C₂×#23984
LCS	G ▷ C₂⁴×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ #23984

23780 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 48

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#6454041, D₃×#6595772, D₃×#6533135, …
maximal normal subgroup of	D₃×#6454041, D₃×#6595772, D₃×#6533135, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.