Finite Group Databasebeta

C22×#65834 #13006070

order1280
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC22×#65834

Splittings

SylowC5 ⋊ C22×#544

Subgroups

subgroupG/H
centerC24C23×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC23×C5×C4⋊C4C2
socleC24×C5C24
prime radicalC25×C5C23
hypercenterC23×C4⋊C4D5
hypocenterC5C22×#544
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C23×C4⋊C4

7630 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, 1076338);