Finite Group Databasebeta

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D₃×#7463 #72245014

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

Splittings

Fitting	C₃×#7463 ⋊ C₂
Sylow	C₃ ⋊ C₂×#7463

Subgroups

	subgroup	G/H
center	C₂²	D₃×#367
commutator	C₃×C₁₆	C₂²×C₈
Frattini	C₄×C₁₆	C₂²×D₃
Fitting	C₃×#7463	C₂
socle	C₂²×C₃	C₂×#367
prime radical	C₂²×D₃	#367
cosocle	C₃×C₄×C₁₆	C₂³
hypercenter	#7463	D₃
hypocenter	C₃	C₂×#7463
LCS	G ▷ C₃×C₁₆ ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #7463

316 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 768

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#151085, D₃×#94754, D₃×#94613, …
maximal normal subgroup of	D₃×#151085, D₃×#94754, D₃×#94613
maximal quotient of	D₃×#94754, C₃⋊D₃×#7463

GAP

Past the SmallGroups library coverage — no SmallGroups id.