Finite Group Databasebeta

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D₃×#13656 #72245463

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

Splittings

Fitting	C₃×#13656 ⋊ C₂
Sylow	C₃ ⋊ C₂×#13656

Subgroups

	subgroup	G/H
center	C₄	C₂×D₃×D₁₆
commutator	C₃×C₁₆	C₂³×C₄
Frattini	C₂×C₁₆	C₂³×D₃
Fitting	C₃×#13656	C₂
socle	C₂×C₃	C₂×C₄×D₁₆
prime radical	D₃×#2262	C₂
cosocle	C₂×C₃×C₁₆	C₂⁴
hypercenter	#13656	D₃
hypocenter	C₃	C₂×#13656
LCS	G ▷ C₃×C₁₆ ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #13656

844 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 192

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#151086, D₃×#153598, D₃×#94613
maximal normal subgroup of	D₃×#151086, D₃×#153598, D₃×#94613

GAP

Past the SmallGroups library coverage — no SmallGroups id.