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AGL(1,𝔽₅)×#953 #14321409

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

AGL(1,𝔽₅)×#953

Splittings

Fitting	C₂⁴×C₃×C₅ ⋊ C₂×C₄
Hall	C₃×C₅ ⋊ C₄×#120
Sylow	C₅ ⋊ C₄×#953
Sylow	C₃ ⋊ AGL(1,𝔽₅)×#120

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₃×AGL(1,𝔽₅)
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₂⁴×C₃×C₅	C₂×C₄
prime radical	D₅×#953	C₂
cosocle	C₂²×C₃×D₅	C₂⁴
hypercenter	C₂⁴	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	C₄×#120
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂⁴

2448 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 120

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×AGL(1,𝔽₅)×#120, AGL(1,𝔽₅)×#5032, AGL(1,𝔽₅)×C₃⋊#1020, …
maximal normal subgroup of	D₃×AGL(1,𝔽₅)×#120, AGL(1,𝔽₅)×#5032
maximal quotient of	AGL(1,𝔽₅)×#5241, AGL(1,𝔽₅)×#5244, AGL(1,𝔽₅)×#64162

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 47107);