Finite Group Databasebeta

D13×#1746 #15860386

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productD13×#1746

Splittings

FittingC13×#1746 ⋊ C2
SylowC13 ⋊ C2×#1746

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D13
commutatorC22×C13C22×C42
FittingC13×#1746C2
socleC23×C13C23×C4
prime radicalC23×D13C22×C4
cosocleC22×C4×C13C24
hypercenter#1746D13
hypocenterC13C2×#1746
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1746

1134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 167035);