Finite Group Databasebeta

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D₃×#10745 #72247698

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂¹⁰

Aliases

Splittings

Fitting	C₃×#10745 ⋊ C₂
Sylow	C₃ ⋊ C₂×#10745

Subgroups

	subgroup	G/H
center	C₂³	D₃×#120
commutator	C₂³×C₃	C₂²×C₄²
Frattini	C₂⁵	C₂³×D₃
Fitting	C₃×#10745	C₂
socle	C₂³×C₃	C₂×#120
prime radical	C₂³×D₃×D₄	C₂²
cosocle	C₂⁵×C₃	C₂⁴
hypercenter	#10745	D₃
hypocenter	C₃	C₂×#10745
LCS	G ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂⁵ ◁ #10745

12668 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 192

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#394066, D₃×#146654, D₃×#147819
maximal normal subgroup of	D₃×#394066, D₃×#146654, D₃×#147819
maximal quotient of	D₃×#146656, D₃×#146654, D₃×#106766

GAP

Past the SmallGroups library coverage — no SmallGroups id.