Finite Group Databasebeta

C22×C13⋊#564 #16769815

order3328
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC22×C13⋊#564

Splittings

SylowC13 ⋊ C22×#564

Subgroups

subgroupG/H
centerC24C23×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC22×C13×#125C2
socle, prime radicalC24×C13C24
hypercenterC22×#125D13
hypocenterC13C22×#564
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×#125

6374 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1076464);