Finite Group Databasebeta

← Prev (#13033112) Next (#13033114) →

AGL(1,𝔽5)×#405 #13033113

order1280
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C22×C43

Aliases

direct productAGL(1,𝔽5)×#405

Splittings

FittingC5×#405 ⋊ C4
SylowC5 ⋊ C4×#405

Subgroups

subgroupG/H
centerC2×C8C22×AGL(1,𝔽5)
commutatorC2×C5C2×C43
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC5×#405C4
socleC22×C5C22×C42
prime radicalC23×D5C22×C4
cosocleC2×C4×D5C24
hypercenter#405AGL(1,𝔽5)
hypocenterC5C4×#405
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C8 ◁ #405

1526 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)×#2875, #72242675, AGL(1,𝔽5)×#2952, …
maximal normal subgroup ofAGL(1,𝔽5)×#2875, AGL(1,𝔽5)×#2952, AGL(1,𝔽5)×#2948, …
maximal quotient of#72242675

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1103381);