Finite Group Databasebeta

← Prev (#13043575) Next (#13043577) →

AGL(1,𝔽5)×#509 #13043576

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,𝔽5)×#509

Splittings

FittingC5×#509 ⋊ C4
SylowC5 ⋊ C4×#509

Subgroups

subgroupG/H
centerC2C2×D8×AGL(1,𝔽5)
commutatorC5×C8C23×C4
FrattiniC8C23×AGL(1,𝔽5)
FittingC5×#509C4
socleC2×C5C2×C4×D8
prime radicalD5×#509C2
cosocleC8×D5C24
hypercenter#509AGL(1,𝔽5)
hypocenterC5C4×#509
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

738 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), #72220781, AGL(1,𝔽5)×#2213, …
maximal normal subgroup ofAGL(1,𝔽5)×AGL(1,ℤ/16), AGL(1,𝔽5)×#2213, C2×AGL(1,𝔽5)×#509, …
maximal quotient of#72220781, AGL(1,𝔽5)×#2177, #509×#1043, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1113844);