Finite Group Databasebeta

← Prev (#12265607) Next (#12265609) →

C2×#10605402 #12265608

order1280
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C27

Aliases

direct productC2×#10605402

Splittings

SylowC5 ⋊ C2×#2402

Subgroups

subgroupG/H
centerC23×C4C22×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C4×C5×C4⋊C4C2
socle, prime radicalC24×C5C24
hypercenterC2×C4×C4⋊C4D5
hypocenterC5C2×#2402
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

2078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1280

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 335876);