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C₂×AGL(1,𝔽₅)×#127 #13043879

order	1280
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

direct product	C₂×AGL(1,𝔽₅)×#127
unambiguous semidirect product	D₅⋊(C₄×#127)

Splittings

Fitting	C₂×C₅×#127 ⋊ C₄
Sylow	C₅ ⋊ C₂×C₄×#127

Subgroups

	subgroup	G/H
center	C₂³	C₂³×AGL(1,𝔽₅)
commutator	C₂²×C₅	C₂⁴×C₄
Frattini	C₂²	C₂⁴×AGL(1,𝔽₅)
Fitting	C₂×C₅×#127	C₄
socle	C₂³×C₅	C₂³×C₄
prime radical	C₂×D₅×#127	C₂
cosocle	C₂²×D₅	C₂⁵
hypercenter	C₂×#127	AGL(1,𝔽₅)
hypocenter	C₅	C₂×C₄×#127
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×#127

5694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 160

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×#127×#1043, AGL(1,𝔽₅)×#3498, AGL(1,𝔽₅)×#2002, …
maximal normal subgroup of	AGL(1,𝔽₅)×#3498, AGL(1,𝔽₅)×#2002, AGL(1,𝔽₅)×#3151, …
maximal quotient of	C₂×#127×#1043, AGL(1,𝔽₅)×#3151, C₂²×AGL(1,𝔽₅)×#127, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1114147);