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C₂×AGL(1,𝔽₅)×#100 #13033360

order	1280
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

C₂×AGL(1,𝔽₅)×#100

Splittings

Fitting	C₂×C₅×#100 ⋊ C₄
Sylow	C₅ ⋊ C₂×C₄×#100

Subgroups

	subgroup	G/H
center	C₂²	C₂²⋊C₄×AGL(1,𝔽₅)
commutator	C₂²×C₅	C₂²×C₄²
Frattini	C₂×C₄	C₂³×AGL(1,𝔽₅)
Fitting	C₂×C₅×#100	C₄
socle	C₂²×C₅	C₄×C₂²⋊C₄
prime radical	C₂²×D₄×D₅	C₂²
cosocle	C₂×C₄×D₅	C₂⁴
hypercenter	C₂×#100	AGL(1,𝔽₅)
hypocenter	C₅	C₂×C₄×#100
LCS	G ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#100

1970 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 80

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×#100×#1043, AGL(1,𝔽₅)×#1914, AGL(1,𝔽₅)×#2002, …
maximal normal subgroup of	AGL(1,𝔽₅)×#1914, AGL(1,𝔽₅)×#2002, AGL(1,𝔽₅)×#3019, …
maximal quotient of	C₂×#100×#1043, C₂×#72221696, #72221767, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1103628);