Finite Group Databasebeta

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D₃×#511793 #72248303

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

Aliases

Splittings

Fitting	C₃×#511793 ⋊ C₂
Sylow	C₃ ⋊ C₂×#511793

Subgroups

	subgroup	G/H
center	C₂	D₃×#32898
commutator, cosocle	C₂²×C₃×D₄	C₂⁵
Frattini	C₂²×D₄	C₂⁴×D₃
Fitting	C₃×#511793	C₂
socle	C₂×C₃	C₂×#32898
hypercenter	#511793	D₃
hypocenter	C₃	C₂×#511793
LCS	G ▷ C₂²×C₃×D₄ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ C₂³×D₄ ◁ #511793

At least 23412 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×#72213329

GAP

Past the SmallGroups library coverage — no SmallGroups id.