Finite Group Databasebeta

← Prev (#72245137) Next (#72245139) →

D₃×#12759 #72245138

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

Splittings

Fitting	C₃×#12759 ⋊ C₂
Sylow	C₃ ⋊ C₂×#12759

Subgroups

	subgroup	G/H
center	C₂²	D₃×B(4,𝔽₂)
commutator	C₂×C₃×D₄	C₂³×C₄
Frattini	C₂²×D₄	C₂³×D₃
Fitting	C₃×#12759	C₂
socle	C₂²×C₃	C₂×B(4,𝔽₂)
prime radical	C₂×D₃×D₄²	C₂
cosocle	C₂²×C₃×D₄	C₂⁴
hypercenter	#12759	D₃
hypocenter	C₃	C₂×#12759
LCS	G ▷ C₂×C₃×D₄ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×D₄ ◁ #12759

11480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 48

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#511771, D₃×#500177, D₃×#501097, …
maximal normal subgroup of	D₃×#511771, D₃×#500177, D₃×#501097, …
maximal quotient of	D₃×#147779

GAP

Past the SmallGroups library coverage — no SmallGroups id.