Finite Group Databasebeta

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AGL(1,𝔽5)×#711 #13107626

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

Aliases

direct productAGL(1,𝔽5)×#711

Splittings

FittingC52×D4 ⋊ C2×C4
SylowC52 ⋊ C4×#41

Subgroups

subgroupG/H
center, FrattiniC2C22×D5×AGL(1,𝔽5)
commutator, socleC2×C52C23×C4
FittingC52×D4C2×C4
prime radicalD5×#711C2
cosocleC2×C5×D5C24
hypercenterD4D5×AGL(1,𝔽5)
hypocenterC52C4×#41
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C2 ◁ D4

640 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 9978);