Finite Group Databasebeta

← Prev (#13027934) Next (#13027936) →

AGL(1,𝔽5)×#380 #13027935

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productAGL(1,𝔽5)×#380

Splittings

FittingC5×#380 ⋊ C4
SylowC5 ⋊ C4×#380

Subgroups

subgroupG/H
center, FrattiniC23C23×AGL(1,𝔽5)
commutatorC22×C5C22×C42
FittingC5×#380C4
socleC23×C5C23×C4
prime radicalC24×D5C23
cosocleC23×D5C24
hypercenter#380AGL(1,𝔽5)
hypocenterC5C4×#380
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ #380

2782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1098203);