Finite Group Databasebeta

C2×#10604248 #13034412

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

Aliases

direct productC2×#10604248

Splittings

SylowC5 ⋊ C2×#1829

Subgroups

subgroupG/H
centerC22#65764
commutatorC23×C5C23×C4
FrattiniC23C23×AGL(1,𝔽5)
FittingC22×C5×C22⋊C4C4
socleC22×C5#381
prime radicalC23×C22⋊D5C22
cosocleC22×Dic5C24
hypercenterC22×C22⋊C4AGL(1,𝔽5)
hypocenterC5C2×#1829
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4

1434 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1104680);