Finite Group Databasebeta

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D₃×#449469 #72253397

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹³

Aliases

Splittings

Fitting	C₃×#449469 ⋊ C₂
Sylow	C₃ ⋊ C₂×#449469

Subgroups

	subgroup	G/H
center	C₂²	D₃×#2403
commutator, cosocle	C₂⁵×C₃	C₂⁵
Frattini	C₂⁵	C₂⁴×D₃
Fitting	C₃×#449469	C₂
socle	C₂²×C₃	C₂×#2403
hypercenter	#449469	D₃
hypocenter	C₃	C₂×#449469
LCS	G ▷ C₂⁵×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ #449469

63882 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 192

Conjugacy classes & character table

186 conjugacy classes — view the full character table.

Relationships

maximal quotient of

D₃×#72219165

GAP

Past the SmallGroups library coverage — no SmallGroups id.