Finite Group Databasebeta

← Prev (#72272062) Next (#72272064) →

D₃×#493474 #72272063

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹²

Aliases

Splittings

Fitting	C₃×#493474 ⋊ C₂
Sylow	C₃ ⋊ C₂×#493474

Subgroups

	subgroup	G/H
center	C₂	D₃×#20585
commutator	C₂⁴×C₃	C₂⁴×C₄
Frattini	C₂²×D₄	C₂⁴×D₃
Fitting	C₃×#493474	C₂
socle	C₂×C₃	C₂×#20585
prime radical	D₃×#62817	C₂
cosocle	C₂²×C₃×D₄	C₂⁵
hypercenter	#493474	D₃
hypocenter	C₃	C₂×#493474
LCS	G ▷ C₂⁴×C₃ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ #3484 ◁ #493474

At least 12970 conjugacy classes of subgroups; only the 2125 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

186 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.