Finite Group Databasebeta

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D₃×#72213329 #72248658

order	6144
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹³

Aliases

D₃×#72213329

Splittings

Fitting	C₃×#72213329 ⋊ C₂
Sylow	C₃ ⋊ C₂×#72213329

Subgroups

	subgroup	G/H
center	C₂²	D₃×#32898
commutator, cosocle	C₂³×C₃×D₄	C₂⁵
Frattini	C₂³×D₄	C₂⁴×D₃
Fitting	C₃×#72213329	C₂
socle	C₂²×C₃	C₂×#32898
hypercenter	#72213329	D₃
hypocenter	C₃	C₂×#72213329
LCS	G ▷ C₂³×C₃×D₄ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂⁴×D₄ ◁ #72213329

Only the 2017 normal subgroups are shown; non-normal subgroups are omitted.

Full subgroup data →

Conjugacy classes & character table

237 conjugacy classes — view the full character table.

Relationships

maximal quotient of

D₃×#72213344

GAP

Past the SmallGroups library coverage — no SmallGroups id.