Finite Group Databasebeta

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D₃×#500168 #72270535

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

Aliases

Splittings

Fitting	C₃×#500168 ⋊ C₂
Sylow	C₃ ⋊ C₂×#500168

Subgroups

	subgroup	G/H
center	C₂	D₃×#24033
commutator, cosocle	C₂²×C₃×C₈	C₂⁵
Frattini	C₂²×C₈	C₂⁴×D₃
Fitting	C₃×#500168	C₂
socle	C₂×C₃	C₂×#24033
prime radical	D₃×#61079	C₂
hypercenter	#500168	D₃
hypocenter	C₃	C₂×#500168
LCS	G ▷ C₂²×C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #2932 ◁ #500168

At least 6868 conjugacy classes of subgroups; only the 933 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.