Finite Group Databasebeta

← Prev (#13044736) Next (#13044738) →

AGL(1,𝔽5)×#575 #13044737

order1280
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productAGL(1,𝔽5)×#575

Splittings

FittingC5×#575 ⋊ C4
SylowC5 ⋊ C4×#575

Subgroups

subgroupG/H
centerC4C2×D4×AGL(1,𝔽5)
commutatorC4×C5C24×C4
FrattiniC4C24×AGL(1,𝔽5)
FittingC5×#575C4
socleC2×C5C22×C4×D4
prime radicalD5×#575C2
cosocleC4×D5C25
hypercenter#575AGL(1,𝔽5)
hypocenterC5C4×#575
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

2842 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 of#72221371, AGL(1,𝔽5)×#3585, AGL(1,𝔽5)×#2010, …
maximal normal subgroup ofAGL(1,𝔽5)×#3585, AGL(1,𝔽5)×#2010, AGL(1,𝔽5)×#2008, …
maximal quotient of#72221371, #72223009, #72223017, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1115005);