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AGL(1,𝔽₅)×#334 #13017292

order	1280
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₈ · Schur multiplier (H₂) = C₂²×C₄

Aliases

AGL(1,𝔽₅)×#334

Splittings

Fitting	C₅×#334 ⋊ C₄
Sylow	C₅ ⋊ C₄×#334

Subgroups

	subgroup	G/H
center	C₂×C₄	D₄×AGL(1,𝔽₅)
commutator	C₄×C₅	C₂×C₄×C₈
Frattini	C₄²	C₂²×AGL(1,𝔽₅)
Fitting	C₅×#334	C₄
socle	C₂²×C₅	C₄×C₄⋊C₄
prime radical	C₂²×D₅	C₂×C₄⋊C₄
cosocle	C₄²×D₅	C₂³
hypercenter	#334	AGL(1,𝔽₅)
hypocenter	C₅	C₄×#334
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ #334

470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 320

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	AGL(1,𝔽₅)×#1368, AGL(1,𝔽₅)×#1580, AGL(1,𝔽₅)×#1333, …
maximal normal subgroup of	AGL(1,𝔽₅)×#1368, AGL(1,𝔽₅)×#1580, AGL(1,𝔽₅)×#1333
maximal quotient of	AGL(1,𝔽₅)×#1368, AGL(1,𝔽₅)×#1369, #334×#1043

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1087560);