Finite Group Databasebeta

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D₃×#13867 #72248201

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹⁴

Aliases

Splittings

Fitting	C₃×#13867 ⋊ C₂
Sylow	C₃ ⋊ C₂×#13867

Subgroups

	subgroup	G/H
center, Frattini	C₂⁴	C₂⁴×D₃
commutator	C₂³×C₃	C₂⁴×C₄
Fitting	C₃×#13867	C₂
socle, cosocle	C₂⁴×C₃	C₂⁵
prime radical	C₂⁴×D₃×D₄	C₂
hypercenter	#13867	D₃
hypocenter	C₃	C₂×#13867
LCS	G ▷ C₂³×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴ ◁ #13867

69092 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 192

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#846041, D₃×#647656, D₃×#187928, …
maximal normal subgroup of	D₃×#846041, D₃×#647656, D₃×#187928, …
maximal quotient of	D₃×#359639, D₃×#359509, D₃×#359472, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.