Finite Group Databasebeta

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D₃×#511819 #72246107

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹²

Aliases

Splittings

Fitting	C₃×#511819 ⋊ C₂
Sylow	C₃ ⋊ C₂×#511819

Subgroups

	subgroup	G/H
center	C₂	D₃×#32898
commutator, cosocle	C₂×C₃×#41	C₂⁵
Frattini	C₂×#41	C₂⁴×D₃
Fitting	C₃×#511819	C₂
socle	C₂×C₃	C₂×#32898
hypercenter	#511819	D₃
hypocenter	C₃	C₂×#511819
LCS	G ▷ C₂×C₃×#41 ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×H(5,𝔽₂) ◁ #511819

At least 16382 conjugacy classes of subgroups; only the 1151 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

159 conjugacy classes — view the full character table.

Relationships

maximal quotient of	D₃×#72215601, D₃×#72214565
automorphism group of	#4557, C₃⋊#338, #5125, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.