Finite Group Databasebeta

C22×#66035 #13006116

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

Aliases

direct productC22×#66035

Splittings

SylowC5 ⋊ C22×#541

Subgroups

subgroupG/H
centerC24C23×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC22×C5×#126C2
socleC24×C5C24
prime radicalC25×C5C23
hypercenterC22×#126D5
hypocenterC5C22×#541
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×#126

7110 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, 1076384);