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C₂²×#64862 #13033153

order	1280
isoclinism	isoclinic class of #3993
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁷

Aliases

Splittings

Fitting	C₂²×C₄²×C₅ ⋊ C₄
Sylow	C₅ ⋊ C₂²×#339

Subgroups

	subgroup	G/H
center	C₂²×C₄	C₄⋊AGL(1,𝔽₅)
commutator	C₄×C₅	C₂²×C₄²
Frattini	C₂×C₄	C₂³×AGL(1,𝔽₅)
Fitting	C₂²×C₄²×C₅	C₄
socle	C₂³×C₅	#95
prime radical	C₂⁴×D₅	D₄
cosocle	C₂×C₄×D₅	C₂⁴
hypercenter	C₂²×C₄²	AGL(1,𝔽₅)
hypocenter	C₅	C₂²×#339
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂²×C₄²

2830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 160

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1103421);