Finite Group Databasebeta

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D₃×#234591 #72255503

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

Aliases

Splittings

Fitting	C₃×#234591 ⋊ C₂
Sylow	C₃ ⋊ C₂×#234591

Subgroups

	subgroup	G/H
center	C₂³	C₂×D₃×#120
commutator, cosocle	C₂³×C₃×C₄	C₂⁵
Frattini	C₂³×C₄	C₂⁴×D₃
Fitting	C₃×#234591	C₂
socle	C₂³×C₃	C₂²×#120
hypercenter	#234591	D₃
hypocenter	C₃	C₂×#234591
LCS	G ▷ C₂³×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂⁴×C₄ ◁ #234591

At least 7558 conjugacy classes of subgroups; only the 1403 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

automorphism group of

C₈×C₃⋊C₈, #4455

GAP

Past the SmallGroups library coverage — no SmallGroups id.