Finite Group Databasebeta

← Prev (#13107614) Next (#13107616) →

AGL(1,𝔽5)×#709 #13107615

order1600
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,𝔽5)×#709

Splittings

FittingC2×C4×C52 ⋊ C2×C4
SylowC52 ⋊ C4×#41

Subgroups

subgroupG/H
centerC4C2×D5×AGL(1,𝔽5)
commutator, socleC2×C52C23×C4
FrattiniC2C22×D5×AGL(1,𝔽5)
FittingC2×C4×C52C2×C4
prime radicalD5×#709C2
cosocleC2×C5×D5C24
hypercenterC2×C4D5×AGL(1,𝔽5)
hypocenterC52C4×#41
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C4 ◁ C2×C4

640 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

130 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 9967);