Finite Group Databasebeta

← Prev (#72255276) Next (#72255278) →

D₃×#7622880 #72255277

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂⁶ · Schur multiplier (H₂) = C₂¹⁵

Aliases

Splittings

Fitting	C₃×#7622880 ⋊ C₂
Sylow	C₃ ⋊ C₂×#7622880

Subgroups

	subgroup	G/H
center	C₂	C₂²×D₃×B(4,𝔽₂)
commutator, cosocle	C₂×C₃×D₄	C₂⁶
Frattini	C₂×D₄	C₂⁵×D₃
Fitting	C₃×#7622880	C₂
socle	C₂×C₃	C₂³×B(4,𝔽₂)
hypercenter	#7622880	D₃
hypocenter	C₃	C₂×#7622880
LCS	G ▷ C₂×C₃×D₄ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₂×D₄ ◁ C₂×H(5,𝔽₂) ◁ #7622880

Only the 4573 normal subgroups are shown; non-normal subgroups are omitted.

Full subgroup data →

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#72217027
automorphism group of	#5237, #5240

GAP

Past the SmallGroups library coverage — no SmallGroups id.