Finite Group Databasebeta

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D₃×#498929 #72253975

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹¹

Aliases

Splittings

Fitting	C₃×#498929 ⋊ C₂
Sylow	C₃ ⋊ C₂×#498929

Subgroups

	subgroup	G/H
center	C₂²	C₂×D₃×B(4,𝔽₂)
commutator, cosocle	C₂²×C₃×D₄	C₂⁵
Frattini	C₂²×D₄	C₂⁴×D₃
Fitting	C₃×#498929	C₂
socle	C₂²×C₃	C₂²×B(4,𝔽₂)
hypercenter	#498929	D₃
hypocenter	C₃	C₂×#498929
LCS	G ▷ C₂²×C₃×D₄ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×#41 ◁ #498929

At least 10332 conjugacy classes of subgroups; only the 1239 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

168 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.