Finite Group Databasebeta

D13×#1680 #15845299

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

direct productD13×#1680

Splittings

FittingC13×#1680 ⋊ C2
SylowC13 ⋊ C2×#1680

Subgroups

subgroupG/H
centerC22D13×#121
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC13×#1680C2
socleC22×C13C2×#121
prime radicalC22×D13#121
hypercenter#1680D13
hypocenterC13C2×#1680
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #1680

670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 151948);