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D₃×#64899 #14294766

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂⁴

Aliases

Splittings

Fitting	C₃×C₅×M₁₆ ⋊ C₂×C₄
Hall	C₃×C₅ ⋊ C₂×#343
Sylow	C₅ ⋊ D₃×#343
Sylow	C₃ ⋊ C₂×#64899

Subgroups

	subgroup	G/H
center	C₂	D₃×(C₂×AGL(1,𝔽₅))⋊C₄
commutator	C₂²×C₃×C₅	C₂×C₄²
Frattini	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×M₁₆	C₂×C₄
socle	C₂×C₃×C₅	C₂×#95
prime radical	C₂²×D₃×D₅	C₂×C₄
cosocle	C₂×C₃×C₄×D₅	C₂³
hypercenter	M₁₆	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	C₂×#343
LCS	G ▷ C₂²×C₃×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

864 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 120

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#10604863, D₃×#10604003, D₃×AGL(1,𝔽₅)×#100
maximal normal subgroup of	D₃×#10604863, D₃×#10604003, D₃×AGL(1,𝔽₅)×#100

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 20464);