Finite Group Databasebeta

← Prev (#13017026) Next (#13017028) →

AGL(1,𝔽5)×#328 #13017027

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

Aliases

direct productAGL(1,𝔽5)×#328

Splittings

FittingC5×#328 ⋊ C4
SylowC5 ⋊ C4×#328

Subgroups

subgroupG/H
centerC22C22⋊C4×AGL(1,𝔽5)
commutatorC2×C4×C5C2×C42
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC5×#328C4
socleC22×C5C4×C22⋊C4
prime radicalC23×D5C2×D4
cosocleC22×C4×D5C23
hypercenter#328AGL(1,𝔽5)
hypocenterC5C4×#328
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

732 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

95 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#1504
maximal normal subgroup ofAGL(1,𝔽5)×#1504

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1087295);