Finite Group Databasebeta

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AGL(1,𝔽5)×#397 #13028088

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productAGL(1,𝔽5)×#397

Splittings

FittingC5×#397 ⋊ C4
SylowC5 ⋊ C4×#397

Subgroups

subgroupG/H
center, FrattiniC23C23×AGL(1,𝔽5)
commutator, socleC23×C5C23×C4
FittingC5×#397C4
prime radicalC24×D5C23
cosocleC23×D5C24
hypercenter#397AGL(1,𝔽5)
hypocenterC5C4×#397
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #397

1790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1098356);