Finite Group Databasebeta

C2×C8×#711 #12963730

order1280
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct productC2×C8×#711

Splittings

FittingC2×C5×C8×D4 ⋊ C2
SylowC5 ⋊ C2×C8×#41

Subgroups

subgroupG/H
centerC22×C8C22×D5
commutatorC2×C5C24×C8
FrattiniC2×C4C24×D5
FittingC2×C5×C8×D4C2
socleC23×C5C23×C4
prime radicalC22×#711C4
cosocleC2×C4×C5C25
hypercenterC2×C8×D4D5
hypocenterC5C2×C8×#41
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C8 ◁ C2×C8×D4

2566 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1033998);