Finite Group Databasebeta

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D₃×#393979 #72272270

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹³

Aliases

Splittings

Fitting	C₃×#393979 ⋊ C₂
Sylow	C₃ ⋊ C₂×#393979

Subgroups

	subgroup	G/H
center	C₂²	C₂×D₃×#392
commutator, cosocle	C₂³×C₃×C₄	C₂⁵
Frattini	C₂³×C₄	C₂⁴×D₃
Fitting	C₃×#393979	C₂
socle	C₂²×C₃	C₂²×#392
hypercenter	#393979	D₃
hypocenter	C₃	C₂×#393979
LCS	G ▷ C₂³×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁴×C₄ ◁ #393979

At least 9816 conjugacy classes of subgroups; only the 1955 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.