Finite Group Databasebeta

C4×#64974 #12097426

order1280
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#64974

Splittings

FittingC42×C5×C8 ⋊ C2
SylowC5 ⋊ C4×#431

Subgroups

subgroupG/H
centerC43C2×D5
commutatorC2×C5C22×C4×C8
FrattiniC22×C4C23×D5
FittingC42×C5×C8C2
socleC23×C5C23×C4
prime radicalC23×D5C22×C4
cosocleC22×C4×C5C24
hypercenterC42×C8D5
hypocenterC5C4×#431
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C43 ◁ C42×C8

1318 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, 167694);