Finite Group Databasebeta

C22×#65937 #13006080

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

Aliases

direct productC22×#65937

Splittings

SylowC5 ⋊ C22×#542

Subgroups

subgroupG/H
centerC24C23×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
Fitting, prime radicalC22×C5×#121C2
socleC24×C5C24
hypercenterC22×#121D5
hypocenterC5C22×#542
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×#121

7974 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1076348);