Finite Group Databasebeta

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D₃×#10993 #72249247

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

Splittings

Fitting	C₃×#10993 ⋊ C₂
Sylow	C₃ ⋊ C₂×#10993

Subgroups

	subgroup	G/H
center	C₂×C₄	D₃×#120
commutator	C₂⁴×C₃	C₂³×C₄
Frattini	C₂³×C₄	C₂³×D₃
Fitting	C₃×#10993	C₂
socle	C₂²×C₃	C₂×#386
prime radical	C₂×D₃×#525	C₂
cosocle	C₂³×C₃×C₄	C₂⁴
hypercenter	#10993	D₃
hypocenter	C₃	C₂×#10993
LCS	G ▷ C₂⁴×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #10993

10228 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#394102, D₃×#449496, D₃×#417674, …
maximal normal subgroup of	D₃×#394102, D₃×#449496, D₃×#417674, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.