Finite Group Databasebeta

D13×#2023 #15890185

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

Aliases

direct productD13×#2023

Splittings

FittingC13×#2023 ⋊ C2
SylowC13 ⋊ C2×#2023

Subgroups

subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2023C2
socleC23×C13C22×D4
prime radicalC22×D4×D13C22
hypercenter#2023D13
hypocenterC13C2×#2023
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2023

1734 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, 196834);