Finite Group Databasebeta

C22×#65244 #12257554

order1280
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C213

Aliases

direct productC22×#65244

Splittings

FittingC23×C5×C22⋊C4 ⋊ C2
SylowC5 ⋊ C22×#379

Subgroups

subgroupG/H
centerC25C22×D5
commutatorC22×C5C24×C4
FrattiniC23C24×D5
FittingC23×C5×C22⋊C4C2
socleC25×C5C23
prime radicalC26×D5C2
cosocleC23×C5C25
hypercenterC23×C22⋊C4D5
hypocenterC5C22×#379
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C25 ◁ C23×C22⋊C4

33214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

272 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 327822);