Finite Group Databasebeta

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D₃×#146479 #72271342

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂¹⁰

Aliases

Splittings

Fitting	C₃×#146479 ⋊ C₂
Sylow	C₃ ⋊ C₂×#146479

Subgroups

	subgroup	G/H
center	C₂²	D₃×#1781
commutator	C₂²×C₃×C₄	C₂²×C₄²
Frattini	C₂³×D₄	C₂³×D₃
Fitting	C₃×#146479	C₂
socle	C₂²×C₃	C₂×#1781
prime radical	C₂⁴×D₃×D₄	C₂²
cosocle	C₂³×C₃×D₄	C₂⁴
hypercenter	#146479	D₃
hypocenter	C₃	C₂×#146479
LCS	G ▷ C₂²×C₃×C₄ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂⁴×D₄ ◁ #146479

43906 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#72219159, D₃×#72218521
maximal normal subgroup of	D₃×#72219159, D₃×#72218521

GAP

Past the SmallGroups library coverage — no SmallGroups id.