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AGL(1,𝔽₅)×AGL(1,ℤ/8) #10617446

order	640
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

AGL(1,𝔽₅)×AGL(1,ℤ/8)

Splittings

Fitting	C₅×AGL(1,ℤ/8) ⋊ C₄
Sylow	C₅ ⋊ C₄×AGL(1,ℤ/8)

Subgroups

	subgroup	G/H
center	C₂	C₂×D₄×AGL(1,𝔽₅)
commutator	C₄×C₅	C₂³×C₄
Frattini	C₄	C₂³×AGL(1,𝔽₅)
Fitting	C₅×AGL(1,ℤ/8)	C₄
socle	C₂×C₅	C₂×C₄×D₄
prime radical	D₅×AGL(1,ℤ/8)	C₂
cosocle	C₄×D₅	C₂⁴
hypercenter	AGL(1,ℤ/8)	AGL(1,𝔽₅)
hypocenter	C₅	C₄×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ AGL(1,ℤ/8)

548 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 40

Conjugacy classes & character table

55 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	AGL(1,𝔽₅)×#453, AGL(1,𝔽₅)×#454, #13036194, …
maximal normal subgroup of	AGL(1,𝔽₅)×#453, AGL(1,𝔽₅)×#454, #13036194, …
maximal quotient of	AGL(1,ℤ/8)×#170, #13031591, #13031592, …
automorphism group of	D₄₀, Dic₂₀, #3993, …
holomorph of	C₅×C₈

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(640, 19528);