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D₃×SD₁₆×AGL(1,𝔽₅) #14416129

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

D₃×SD₁₆×AGL(1,𝔽₅)

Splittings

Fitting	C₃×C₅×SD₁₆ ⋊ C₂×C₄
Hall	C₃×C₅ ⋊ C₂×C₄×SD₁₆
Sylow	C₅ ⋊ C₄×D₃×SD₁₆
Sylow	C₃ ⋊ C₂×SD₁₆×AGL(1,𝔽₅)

Subgroups

	subgroup	G/H
center	C₂	D₃×D₄×AGL(1,𝔽₅)
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₄	C₂²×D₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×SD₁₆	C₂×C₄
socle	C₂×C₃×C₅	C₂×C₄×D₄
prime radical	D₃×D₄×D₅	C₂²
cosocle	C₃×C₄×D₅	C₂⁴
hypercenter	SD₁₆	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	C₂×C₄×SD₁₆
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

1104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 120

Conjugacy classes & character table

105 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×AGL(1,𝔽₅)×AGL(1,ℤ/8), AGL(1,𝔽₅)×#63930, D₃×#13104059, …
maximal normal subgroup of	D₃×AGL(1,𝔽₅)×AGL(1,ℤ/8)
maximal quotient of	AGL(1,𝔽₅)×#63930, D₃×#13104059, D₃×AGL(1,𝔽₅)×#106

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 141827);