Finite Group Databasebeta

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D₃×#10576928 #72253995

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂⁷ · Schur multiplier (H₂) = C₂¹⁹

Aliases

D₃×#10576928

Splittings

Fitting	C₃×#10576928 ⋊ C₂
Sylow	C₃ ⋊ C₂×#10576928

Subgroups

	subgroup	G/H
center	C₂²	C₂⁴×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁷
Frattini	C₂×C₄	C₂⁶×D₃
Fitting	C₃×#10576928	C₂
socle	C₂²×C₃	C₂⁵×D₄
hypercenter	#10576928	D₃
hypocenter	C₃	C₂×#10576928
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #3444 ◁ #10576928

Only the 35235 normal subgroups are shown; non-normal subgroups are omitted.

Full subgroup data →

Conjugacy classes & character table

312 conjugacy classes. The character table is too large to display.

Relationships

automorphism group of

C₂×#800, C₂×#826, C₂×#827, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.