Finite Group Databasebeta

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D₃×#394602 #72270435

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹¹

Aliases

Splittings

Fitting	C₃×#394602 ⋊ C₂
Sylow	C₃ ⋊ C₂×#394602

Subgroups

	subgroup	G/H
center	C₂²	C₂×D₃×#394
commutator, cosocle	C₂³×C₃×C₄	C₂⁵
Frattini	C₂³×C₄	C₂⁴×D₃
Fitting	C₃×#394602	C₂
socle	C₂²×C₃	C₂²×#394
prime radical	C₂×D₃×#3003	C₂
hypercenter	#394602	D₃
hypocenter	C₃	C₂×#394602
LCS	G ▷ C₂³×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁴×C₄ ◁ #394602

At least 8862 conjugacy classes of subgroups; only the 1651 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#72215520
maximal normal subgroup of	D₃×#72215520

GAP

Past the SmallGroups library coverage — no SmallGroups id.