Finite Group Databasebeta

C2×#10604881 #13029226

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

Aliases

direct productC2×#10604881

Splittings

SylowC5 ⋊ C2×#1463

Subgroups

subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC23×C5C23×C4
FrattiniC23C23×AGL(1,𝔽5)
FittingC24×C4×C5C4
socleC23×C5C2×C22⋊C4
prime radicalC25×C5C2×C4
cosocleC22×Dic5C24
hypercenterC24×C4AGL(1,𝔽5)
hypocenterC5C2×#1463
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C25 ◁ C24×C4

1718 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1099494);