Finite Group Databasebeta

C4×#64732 #12014127

order1280
isoclinismisoclinic class of #64686
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C42

Aliases

direct productC4×#64732

Splittings

SylowC5 ⋊ C4×#347

Subgroups

subgroupG/H
centerC42C4×Dic5
commutatorC4×C5C43
FrattiniC22×C8C22×D5
FittingC4×C5×M32C2
socleC22×C5C2×#97
prime radicalC23×C5C2×M16
cosocleC22×C5×C8C23
hypercenterC4×M32D5
hypocenterC5C4×#347
LCSG ▷ C4×C5 ▷ C5
UCSC1 ◁ C42 ◁ C4×M32

418 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 84395);