Finite Group Databasebeta

C8×#4047 #12064885

order1280
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC8×#4047

Splittings

FittingC2×C5×C82 ⋊ C2
SylowC5 ⋊ C8×#131

Subgroups

subgroupG/H
centerC82C2×D5
commutatorC2×C5C22×C4×C8
FrattiniC42C23×D5
FittingC2×C5×C82C2
socleC22×C5C22×C42
prime radicalC2×#709C2×C4
cosocleC42×C5C24
hypercenterC2×C82D5
hypocenterC5C8×#131
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C82 ◁ C2×C82

922 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 135153);