Finite Group Databasebeta

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C₂×D₃×#33551 #72248600

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

Aliases

C₂×D₃×#33551

Splittings

Fitting	C₂×C₃×#33551 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#33551

Subgroups

	subgroup	G/H
center	C₂²	C₂×D₃×B(4,𝔽₂)
commutator, cosocle	C₂×C₃×D₄	C₂⁶
Frattini	C₂×D₄	C₂⁵×D₃
Fitting	C₂×C₃×#33551	C₂
socle	C₂²×C₃	C₂²×B(4,𝔽₂)
hypercenter	C₂×#33551	D₃
hypocenter	C₃	C₂²×#33551
LCS	G ▷ C₂×C₃×D₄ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂³×D₄ ◁ C₂×#33551

At least 17142 conjugacy classes of subgroups; only the 4583 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#72213329, C₂×D₃×#511790
maximal normal subgroup of	D₃×#72213329, C₂×D₃×#511790
maximal quotient of	D₃×#72210575

GAP

Past the SmallGroups library coverage — no SmallGroups id.