Finite Group Databasebeta

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D₃×#146488 #72255367

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁹

Aliases

Splittings

Fitting	C₃×#146488 ⋊ C₂
Sylow	C₃ ⋊ C₂×#146488

Subgroups

	subgroup	G/H
center	C₂²	D₃×#1781
commutator	C₂²×C₃×C₄	C₂²×C₄²
Frattini	C₂²×#41	C₂³×D₃
Fitting	C₃×#146488	C₂
socle	C₂²×C₃	C₂×#1781
prime radical	C₂²×D₃×H(5,𝔽₂)	C₂²
cosocle	C₂²×C₃×#41	C₂⁴
hypercenter	#146488	D₃
hypocenter	C₃	C₂×#146488
LCS	G ▷ C₂²×C₃×C₄ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×H(5,𝔽₂) ◁ #146488

At least 6900 conjugacy classes of subgroups; only the 1287 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#72214565
maximal normal subgroup of	D₃×#72214565

GAP

Past the SmallGroups library coverage — no SmallGroups id.