Finite Group Databasebeta

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D₃×#499269 #72271666

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁹

Aliases

Splittings

Fitting	C₃×#499269 ⋊ C₂
Sylow	C₃ ⋊ C₂×#499269

Subgroups

	subgroup	G/H
center	C₂	D₃×#23573
commutator, cosocle	C₂²×C₃×C₈	C₂⁵
Frattini	C₂²×C₈	C₂⁴×D₃
Fitting	C₃×#499269	C₂
socle	C₂×C₃	C₂×#23573
hypercenter	#499269	D₃
hypocenter	C₃	C₂×#499269
LCS	G ▷ C₂²×C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #2875 ◁ #499269

At least 7962 conjugacy classes of subgroups; only the 859 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

159 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.