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AGL(1,𝔽₅)×#443 #13033802

order	1280
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

AGL(1,𝔽₅)×#443

Splittings

Fitting	C₅×#443 ⋊ C₄
Sylow	C₅ ⋊ C₄×#443

Subgroups

	subgroup	G/H
center	C₈	D₄×AGL(1,𝔽₅)
commutator	C₄×C₅	C₂²×C₄²
Frattini	C₂×C₄	C₂³×AGL(1,𝔽₅)
Fitting	C₅×#443	C₄
socle	C₂×C₅	C₄²×D₄
prime radical	D₅×#135	C₂²
cosocle	C₂×C₄×D₅	C₂⁴
hypercenter	#443	AGL(1,𝔽₅)
hypocenter	C₅	C₄×#443
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ #443

1046 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 80

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	AGL(1,𝔽₅)×#3292, AGL(1,𝔽₅)×#3291, AGL(1,𝔽₅)×#2956, …
maximal normal subgroup of	AGL(1,𝔽₅)×#3292, AGL(1,𝔽₅)×#3291, AGL(1,𝔽₅)×#2956, …
maximal quotient of	#72223022, #72223458

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1104070);