Finite Group Databasebeta

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D₃×#15266 #72248231

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹²

Aliases

Splittings

Fitting	C₃×#15266 ⋊ C₂
Sylow	C₃ ⋊ C₂×#15266

Subgroups

	subgroup	G/H
center, Frattini	C₂⁴	C₂⁴×D₃
commutator, socle, cosocle	C₂⁴×C₃	C₂⁵
Fitting	C₃×#15266	C₂
prime radical	C₂²×D₃×#120	C₂
hypercenter	#15266	D₃
hypocenter	C₃	C₂×#15266
LCS	G ▷ C₂⁴×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴ ◁ #15266

30324 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×#850465, D₃×#1420724, …
maximal normal subgroup of	D₃×#846041, D₃×#850465, D₃×#1420724, …
maximal quotient of	D₃×#418876

GAP

Past the SmallGroups library coverage — no SmallGroups id.