Finite Group Databasebeta

C22×#65268 #12265490

order1280
isoclinismisoclinic class of #64945
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC22×#65268

Splittings

SylowC5 ⋊ C22×#395

Subgroups

subgroupG/H
centerC25C22×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC23×C5×C4⋊C4C2
socle, prime radicalC25×C5C23
hypercenterC23×C4⋊C4D5
hypocenterC5C22×#395
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C25 ◁ C23×C4⋊C4

6046 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1280

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, 335758);