Finite Group Databasebeta

C2×#10619413 #13046034

order1280
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC2×#10619413

Splittings

SylowC5 ⋊ C2×#3573

Subgroups

subgroupG/H
centerC22C24×AGL(1,𝔽5)
commutatorC2×C5C25×C4
FrattiniC2C25×AGL(1,𝔽5)
FittingC2×C5×H(5,𝔽2)C4
socleC22×C5C24×C4
prime radicalC2×#66285C2
cosocleDic5C26
hypercenterC2×H(5,𝔽2)AGL(1,𝔽5)
hypocenterC5C2×#3573
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×H(5,𝔽2)

10858 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1116302);