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AGL(1,𝔽5)×#431 #13033608

order1280
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C23×C42

Aliases

direct productAGL(1,𝔽5)×#431

Splittings

FittingC5×#431 ⋊ C4
SylowC5 ⋊ C4×#431

Subgroups

subgroupG/H
centerC42C22×AGL(1,𝔽5)
commutatorC2×C5C22×C4×C8
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC5×#431C4
socleC22×C5C22×C42
prime radicalC23×D5C22×C4
cosocleC2×C4×D5C24
hypercenter#431AGL(1,𝔽5)
hypocenterC5C4×#431
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C42 ◁ #431

1318 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#2968
maximal normal subgroup ofAGL(1,𝔽5)×#2968

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1103876);