Finite Group Databasebeta

D13×#2000 #15889705

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productD13×#2000

Splittings

FittingC13×#2000 ⋊ C2
SylowC13 ⋊ C2×#2000

Subgroups

subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2000C2
socleC23×C13C22×D4
prime radicalC2×D13×#121C2
hypercenter#2000D13
hypocenterC13C2×#2000
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

2526 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

256 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 196354);