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AGL(1,𝔽5)×#472 #13036383

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,𝔽5)×#472

Splittings

FittingC5×#472 ⋊ C4
SylowC5 ⋊ C4×#472

Subgroups

subgroupG/H
centerC2AGL(1,𝔽5)×#121
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC5×#472C4
socleC2×C5C4×#121
prime radicalD5×#472C2
cosocleC2×C4×D5C24
hypercenter#472AGL(1,𝔽5)
hypocenterC5C4×#472
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ #472

946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#3292, AGL(1,𝔽5)×#3288, AGL(1,𝔽5)×#3068, …
maximal normal subgroup ofAGL(1,𝔽5)×#3292, AGL(1,𝔽5)×#3288, AGL(1,𝔽5)×#3068
maximal quotient of#72223479, #72226384, #72226562

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1106651);