Finite Group Databasebeta

C5×#65828 #13106648

order1600
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#65828

Splittings

FittingC2×C52×C22⋊C4 ⋊ C2
SylowC52 ⋊ #538

Subgroups

subgroupG/H
centerC22×C5C23×D5
commutator, cosocleC22×C5C24×C5
FrattiniC22C23×C5×D5
FittingC2×C52×C22⋊C4C2
socleC22×C52C24
hypercenterC2×C5×C22⋊C4D5
hypocenterC5C5×#538
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C5 ◁ C2×C5×C22⋊C4

632 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 9000);