Finite Group Databasebeta

C22×#65236 #12265480

order1280
isoclinismisoclinic class of #64945
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C211

Aliases

direct productC22×#65236

Splittings

SylowC5 ⋊ C22×#393

Subgroups

subgroupG/H
centerC25C22×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC23×C5×C22⋊C4C2
socleC25×C5C23
prime radicalC26×C5C22
hypercenterC23×C22⋊C4D5
hypocenterC5C22×#393
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C25 ◁ C23×C22⋊C4

7118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

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, 335748);