Finite Group Databasebeta

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D₃×#10785 #72249238

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁹

Aliases

Splittings

Fitting	C₃×#10785 ⋊ C₂
Sylow	C₃ ⋊ C₂×#10785

Subgroups

	subgroup	G/H
center	C₂²	D₃×#386
commutator	C₂×C₃×C₄	C₂²×C₄²
Frattini	C₂³×C₄	C₂³×D₃
Fitting	C₃×#10785	C₂
socle	C₂²×C₃	C₂×#386
prime radical	C₂³×D₃×D₄	C₂²
cosocle	C₂³×C₃×C₄	C₂⁴
hypercenter	#10785	D₃
hypocenter	C₃	C₂×#10785
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #10785

9780 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#394102, D₃×#374114, D₃×#364592, …
maximal normal subgroup of	D₃×#394102, D₃×#374114, D₃×#364592, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.