Finite Group Databasebeta

← Prev (#13025897) Next (#13025899) →

AGL(1,𝔽5)×#360 #13025898

order1280
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productAGL(1,𝔽5)×#360

Splittings

FittingC5×#360 ⋊ C4
SylowC5 ⋊ C4×#360

Subgroups

subgroupG/H
centerC2AGL(1,𝔽5)×#102
commutatorC5×C8C2×C42
FrattiniC2×C8C22×AGL(1,𝔽5)
FittingC5×#360C4
socleC2×C5C4×#102
prime radicalD5×#135C22
cosocleC2×C8×D5C23
hypercenter#360AGL(1,𝔽5)
hypocenterC5C4×#360
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

466 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)×AGL(1,ℤ/16), #72220797, AGL(1,𝔽5)×#2230, …
maximal normal subgroup ofAGL(1,𝔽5)×AGL(1,ℤ/16), AGL(1,𝔽5)×#2230, C2×AGL(1,𝔽5)×#360, …
maximal quotient of#72220797, AGL(1,𝔽5)×#1333, C2×AGL(1,𝔽5)×#360, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1096166);