Finite Group Databasebeta

C2×#10599815 #12128244

order1280
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#10599815

Splittings

SylowC5 ⋊ C2×#2082

Subgroups

subgroupG/H
centerC22#64963
commutator, cosocleC22×C4×C5C24
FrattiniC22×C4C23×D5
FittingC2×C5×#344C2
socleC22×C5#397
prime radicalC24×C5#41
hypercenterC2×#344D5
hypocenterC5C2×#2082
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#344

878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

134 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 198512);