Finite Group Databasebeta

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D₃×#7307 #72230388

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

Splittings

Fitting	C₃×#7307 ⋊ C₂
Sylow	C₃ ⋊ C₂×#7307

Subgroups

	subgroup	G/H
center	C₂²	D₃×#342
commutator	C₂²×C₃×C₄	C₂×C₄²
Frattini	C₂³×D₄	C₂²×D₃
Fitting	C₃×#7307	C₂
socle	C₂²×C₃	C₂×#342
prime radical	C₂³×D₃×D₄	C₂²
cosocle	C₂³×C₃×D₄	C₂³
hypercenter	#7307	D₃
hypocenter	C₃	C₂×#7307
LCS	G ▷ C₂²×C₃×C₄ ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂³×D₄ ◁ #7307

5116 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 48

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#144366, D₃×#139743, C₂×D₃×#7307, …
maximal normal subgroup of	D₃×#144366, D₃×#139743, C₂×D₃×#7307, …
maximal quotient of	C₂×D₃×#7307

GAP

Past the SmallGroups library coverage — no SmallGroups id.