Finite Group Databasebeta

← Prev (#13027520) Next (#13027522) →

AGL(1,𝔽₅)×M₆₄ #13027521

order	1280
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₆ · Schur multiplier (H₂) = C₂×C₄

Aliases

AGL(1,𝔽₅)×M₆₄

Splittings

Fitting	C₅×M₆₄ ⋊ C₄
Sylow	C₅ ⋊ C₄×M₆₄

Subgroups

	subgroup	G/H
center, Frattini	C₁₆	C₂²×AGL(1,𝔽₅)
commutator, socle	C₂×C₅	C₂×C₄×C₁₆
Fitting	C₅×M₆₄	C₄
prime radical	C₂²×D₅	C₂×C₁₆
cosocle	D₅×C₁₆	C₂³
hypercenter	M₆₄	AGL(1,𝔽₅)
hypocenter	C₅	C₄×M₆₄
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₁₆ ◁ M₆₄

250 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 160

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	AGL(1,𝔽₅)×#1398, AGL(1,𝔽₅)×#2263, AGL(1,𝔽₅)×#1426, …
maximal normal subgroup of	AGL(1,𝔽₅)×#1398, AGL(1,𝔽₅)×#2263, AGL(1,𝔽₅)×#1426, …
maximal quotient of	#72242245, #72269160

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1097789);