Finite Group Databasebeta

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D₃×#15283 #72248223

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹⁰×C₄

Aliases

Splittings

Fitting	C₃×#15283 ⋊ C₂
Sylow	C₃ ⋊ C₂×#15283

Subgroups

	subgroup	G/H
center, Frattini	C₂⁴	C₂⁴×D₃
commutator, socle, cosocle	C₂⁴×C₃	C₂⁵
Fitting	C₃×#15283	C₂
prime radical	C₂²×D₃×#120	C₂
hypercenter	#15283	D₃
hypocenter	C₃	C₂×#15283
LCS	G ▷ C₂⁴×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴ ◁ #15283

29148 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 192

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#846041, D₃×#619101, D₃×#1260433, …
maximal normal subgroup of	D₃×#846041, D₃×#619101, D₃×#1260433, …
maximal quotient of	D₃×#421068

GAP

Past the SmallGroups library coverage — no SmallGroups id.