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AGL(1,𝔽5)×#560 #13044194

order1280
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productAGL(1,𝔽5)×#560

Splittings

FittingC5×#560 ⋊ C4
SylowC5 ⋊ C4×#560

Subgroups

subgroupG/H
center, FrattiniC22C24×AGL(1,𝔽5)
commutator, socleC22×C5C24×C4
FittingC5×#560C4
prime radicalD5×#560C2
cosocleC22×D5C25
hypercenter#560AGL(1,𝔽5)
hypocenterC5C4×#560
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #560

2568 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

95 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#3532, AGL(1,𝔽5)×#2200, AGL(1,𝔽5)×#560⋊C3
maximal normal subgroup ofAGL(1,𝔽5)×#3532, AGL(1,𝔽5)×#2200, AGL(1,𝔽5)×#560⋊C3
maximal quotient ofAGL(1,𝔽5)×#2669

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1114462);