Finite Group Databasebeta

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D₃×#11717055 #72259479

order	4800
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

D₃×#11717055

Splittings

Hall	C₃×C₅² ⋊ C₂×AGL(1,ℤ/8)
Sylow	C₅² ⋊ D₃×AGL(1,ℤ/8)
Sylow	C₃ ⋊ C₂×#11717055

Subgroups

	subgroup	G/H
center	C₂	D₃×#87886
commutator, cosocle	C₃×C₄×C₅²	C₂⁴
Frattini	C₄	C₂×D₃×D₅²
Fitting	C₃×C₅²×D₄	C₂³
socle	C₂×C₃×C₅²	C₂²×D₄
hypercenter	D₄	D₃×D₅²
hypocenter	C₃×C₅²	C₂×AGL(1,ℤ/8)
LCS	G ▷ C₃×C₄×C₅² ▷ C₂×C₃×C₅² ▷ C₃×C₅²
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₄

1664 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 120

Conjugacy classes & character table

177 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#13106298
maximal normal subgroup of	D₃×#13106298

GAP

Past the SmallGroups library coverage — no SmallGroups id.