Finite Group Databasebeta

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D₃×#144415 #72255267

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁸

Aliases

Splittings

Fitting	C₃×#144415 ⋊ C₂
Sylow	C₃ ⋊ C₂×#144415

Subgroups

	subgroup	G/H
center	C₂²	D₃×#2021
commutator, cosocle	C₂³×C₃×D₄	C₂⁴
Frattini	C₂³×D₄	C₂³×D₃
Fitting	C₃×#144415	C₂
socle	C₂²×C₃	C₂×#2021
prime radical	D₃×#3484	C₂²
hypercenter	#144415	D₃
hypocenter	C₃	C₂×#144415
LCS	G ▷ C₂³×C₃×D₄ ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂³×D₄ ◁ #144415

At least 7064 conjugacy classes of subgroups; only the 305 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#72213293
maximal normal subgroup of	D₃×#72213293

GAP

Past the SmallGroups library coverage — no SmallGroups id.