Finite Group Databasebeta

← Prev (#72258507) Next (#72258509) →

D₃×#212918 #72258508

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹×C₈

Aliases

Splittings

Fitting	C₃×#212918 ⋊ C₂
Sylow	C₃ ⋊ C₂×#212918

Subgroups

	subgroup	G/H
center	C₂³	C₂×D₃×#127
commutator	C₃×C₄²	C₂⁴×C₄
Frattini	C₂×C₄²	C₂⁴×D₃
Fitting	C₃×#212918	C₂
socle	C₂³×C₃	C₂²×#127
prime radical	C₂×D₃×#1712	C₂
cosocle	C₂×C₃×C₄²	C₂⁵
hypercenter	#212918	D₃
hypocenter	C₃	C₂×#212918
LCS	G ▷ C₃×C₄² ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #212918

15570 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 768

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.