Finite Group Databasebeta

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D₃×#511827 #72247971

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

Aliases

Splittings

Fitting	C₃×#511827 ⋊ C₂
Sylow	C₃ ⋊ C₂×#511827

Subgroups

	subgroup	G/H
center	C₂	D₃×#32898
commutator, cosocle	C₂×C₃×#41	C₂⁵
Frattini	C₂×#41	C₂⁴×D₃
Fitting	C₃×#511827	C₂
socle	C₂×C₃	C₂×#32898
hypercenter	#511827	D₃
hypocenter	C₃	C₂×#511827
LCS	G ▷ C₂×C₃×#41 ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×H(5,𝔽₂) ◁ #511827

At least 26952 conjugacy classes of subgroups; only the 1151 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal quotient of

D₃×#72215601

GAP

Past the SmallGroups library coverage — no SmallGroups id.