Finite Group Databasebeta

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D₃×#34258 #72255333

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₄ · Schur multiplier (H₂) = C₂¹⁵

Aliases

Splittings

Fitting	C₃×#34258 ⋊ C₂
Sylow	C₃ ⋊ C₂×#34258

Subgroups

	subgroup	G/H
center, Frattini	C₂³	C₂⁵×D₃
commutator	C₂²×C₃	C₂⁵×C₄
Fitting	C₃×#34258	C₂
socle, cosocle	C₂³×C₃	C₂⁶
prime radical	C₂²×D₃×H(5,𝔽₂)	C₂
hypercenter	#34258	D₃
hypocenter	C₃	C₂×#34258
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ #34258

51156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 192

Conjugacy classes & character table

264 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃×#146488, D₃×#7659307, D₃×#359573
maximal normal subgroup of	D₃×#146488, D₃×#7659307, D₃×#359573
maximal quotient of	D₃×#517592

GAP

Past the SmallGroups library coverage — no SmallGroups id.