Finite Group Databasebeta

← Prev (#13036334) Next (#13036336) →

AGL(1,𝔽5)×#466 #13036335

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productAGL(1,𝔽5)×#466

Splittings

FittingC5×#466 ⋊ C4
SylowC5 ⋊ C4×#466

Subgroups

subgroupG/H
centerC22C2×D4×AGL(1,𝔽5)
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC5×#466C4
socleC22×C5C2×C4×D4
prime radicalD5×#466C2
cosocleC2×C4×D5C24
hypercenter#466AGL(1,𝔽5)
hypocenterC5C4×#466
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

1222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#3058, #72253330, #72253346
maximal normal subgroup ofAGL(1,𝔽5)×#3058
maximal quotient of#72253330, #72253346

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1106603);