Finite Group Databasebeta

← Prev (#13044195) Next (#13044197) →

AGL(1,𝔽₅)×H(3,𝔽₄) #13044196

order	1280
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁶×C₄²

Aliases

AGL(1,𝔽₅)×H(3,𝔽₄)

Splittings

Fitting	C₅×H(3,𝔽₄) ⋊ C₄
Sylow	C₅ ⋊ C₄×H(3,𝔽₄)

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×AGL(1,𝔽₅)
commutator, socle	C₂²×C₅	C₂⁴×C₄
Fitting	C₅×H(3,𝔽₄)	C₄
prime radical	D₅×H(3,𝔽₄)	C₂
cosocle	C₂²×D₅	C₂⁵
hypercenter	H(3,𝔽₄)	AGL(1,𝔽₅)
hypocenter	C₅	C₄×H(3,𝔽₄)
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ H(3,𝔽₄)

2664 conjugacy classes of subgroups; only the 776 normal subgroups are shown.

normal subgroups only

This group has 2664 conjugacy classes of subgroups — too many to draw. Only its 776 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 80

Conjugacy classes & character table

95 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	AGL(1,𝔽₅)×#5464, AGL(1,𝔽₅)×#3532, AGL(1,𝔽₅)×#2199, …
maximal normal subgroup of	AGL(1,𝔽₅)×#5464, AGL(1,𝔽₅)×#3532, AGL(1,𝔽₅)×#2199, …
maximal quotient of	AGL(1,𝔽₅)×#2679

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1114464);