Finite Group Databasebeta

C2×#10603928 #13034778

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#10603928

Splittings

SylowC5 ⋊ C2×#1858

Subgroups

subgroupG/H
centerC22#65699
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC2×C5×#100C4
socleC22×C5#385
prime radicalC22×#711C22
cosocleC2×C4×D5C24
hypercenterC2×#100AGL(1,𝔽5)
hypocenterC5C2×#1858
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

1310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1105046);