Finite Group Databasebeta

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D₃×#147813 #72270918

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

Splittings

Fitting	C₃×#147813 ⋊ C₂
Sylow	C₃ ⋊ C₂×#147813

Subgroups

	subgroup	G/H
center	C₂²	D₃×#1790
commutator	C₂²×C₃×D₄	C₂³×C₄
Frattini	C₂²×#41	C₂³×D₃
Fitting	C₃×#147813	C₂
socle	C₂²×C₃	C₂×#1790
prime radical	D₃×#37269	C₂
cosocle	C₂²×C₃×#41	C₂⁴
hypercenter	#147813	D₃
hypocenter	C₃	C₂×#147813
LCS	G ▷ C₂²×C₃×D₄ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×#41 ◁ #147813

At least 8378 conjugacy classes of subgroups; only the 839 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#72214565
maximal normal subgroup of	D₃×#72214565

GAP

Past the SmallGroups library coverage — no SmallGroups id.