Finite Group Databasebeta

C5×#65014 #13101987

order1600
automorphism?
homologyAbelianization (H1) = C22×C5×C8 · Schur multiplier (H2) = C23

Aliases

direct productC5×#65014

Splittings

FittingC52×C22⋊C8 ⋊ C2
SylowC52 ⋊ C8×D4

Subgroups

subgroupG/H
centerC2×C4×C5C22×D5
commutatorC2×C5C22×C5×C8
FrattiniC2×C4C22×C5×D5
FittingC52×C22⋊C8C2
socleC22×C52C22×C4
prime radicalC2×C5×C22⋊D5C4
cosocleC2×C4×C5C23×C5
hypercenterC5×C22⋊C8D5
hypocenterC5C5×C8×D4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4×C5 ◁ C5×C22⋊C8

318 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 4339);