Finite Group Databasebeta

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D₃×#394022 #72271751

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹³

Aliases

Splittings

Fitting	C₃×#394022 ⋊ C₂
Sylow	C₃ ⋊ C₂×#394022

Subgroups

	subgroup	G/H
center	C₂²	D₃×#2403
commutator, cosocle	C₂³×C₃×C₄	C₂⁵
Frattini	C₂³×C₄	C₂⁴×D₃
Fitting	C₃×#394022	C₂
socle	C₂²×C₃	C₂×#2403
hypercenter	#394022	D₃
hypocenter	C₃	C₂×#394022
LCS	G ▷ C₂³×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #394022

At least 10414 conjugacy classes of subgroups; only the 1935 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.