Finite Group Databasebeta

C5×#65016 #13101989

order1600
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#65016

Splittings

FittingC52×C22⋊C8 ⋊ C2
SylowC52 ⋊ #408

Subgroups

subgroupG/H
centerC2×C4×C5C22×D5
commutatorC22×C5C22×C4×C5
FrattiniC2×C4C22×C5×D5
FittingC52×C22⋊C8C2
socleC22×C52C22×C4
prime radicalC2×C5×#709C2
cosocleC2×C4×C5C23×C5
hypercenterC5×C22⋊C8D5
hypocenterC5C5×#408
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4×C5 ◁ C5×C22⋊C8

366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 4341);