Finite Group Databasebeta

C2×#10598668 #13025510

order1280
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#10598668

Splittings

SylowC5 ⋊ C2×#1385

Subgroups

subgroupG/H
centerC2×C4#3993
commutatorC5×C8C2×C42
FrattiniC2×C8C22×AGL(1,𝔽5)
FittingC22×C5×C16C4
socleC22×C5#340
prime radicalC23×D5Q16
cosocleC2×C8×D5C23
hypercenterC22×C16AGL(1,𝔽5)
hypocenterC5C2×#1385
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

554 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, 1095778);