Finite Group Databasebeta

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D₃×#498931 #72248452

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

Aliases

Splittings

Fitting	C₃×#498931 ⋊ C₂
Sylow	C₃ ⋊ C₂×#498931

Subgroups

	subgroup	G/H
center	C₂²	C₂×D₃×B(4,𝔽₂)
commutator, cosocle	C₂²×C₃×D₄	C₂⁵
Frattini	C₂²×D₄	C₂⁴×D₃
Fitting	C₃×#498931	C₂
socle	C₂²×C₃	C₂²×B(4,𝔽₂)
hypercenter	#498931	D₃
hypocenter	C₃	C₂×#498931
LCS	G ▷ C₂²×C₃×D₄ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂³×D₄ ◁ #498931

At least 13132 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×#72213329
maximal normal subgroup of	D₃×#72213329
maximal quotient of	D₃×#72213293

GAP

Past the SmallGroups library coverage — no SmallGroups id.