Finite Group Databasebeta

C4×#64758 #11990179

order1280
isoclinismisoclinic class of #64757
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#64758

Splittings

SylowC5 ⋊ C4×#328

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic5
commutatorC2×C4×C5C2×C42
FrattiniC23×C4C22×D5
FittingC4×C5×C22⋊Q8C2
socleC23×C5C2×C22⋊C4
prime radicalC24×C5C2×D4
cosocleC23×C4×C5C23
hypercenterC4×C22⋊Q8D5
hypocenterC5C4×#328
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊Q8

732 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

188 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 60447);