Finite Group Databasebeta

← Prev (#13033367) Next (#13033369) →

AGL(1,𝔽5)×#413 #13033368

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productAGL(1,𝔽5)×#413

Splittings

FittingC5×#413 ⋊ C4
SylowC5 ⋊ C4×#413

Subgroups

subgroupG/H
centerC4C22⋊C4×AGL(1,𝔽5)
commutatorC22×C5C22×C42
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC5×#413C4
socleC2×C5C2×C4×C22⋊C4
prime radicalC2×D5×#41C22
cosocleC2×C4×D5C24
hypercenter#413AGL(1,𝔽5)
hypocenterC5C4×#413
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

1570 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#1891, AGL(1,𝔽5)×#1914, AGL(1,𝔽5)×#3021, …
maximal normal subgroup ofAGL(1,𝔽5)×#1891, AGL(1,𝔽5)×#1914, AGL(1,𝔽5)×#3021, …
maximal quotient of#72221724, #72226399, #72226579

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1103636);