Finite Group Databasebeta

D13×#1591 #15832657

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productD13×#1591

Splittings

FittingC13×#1591 ⋊ C2
SylowC13 ⋊ C2×#1591

Subgroups

subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1591C2
socleC22×C13C2×C4×D4
prime radicalC22×D13C4×D4
cosocleC42×C13C24
hypercenter#1591D13
hypocenterC13C2×#1591
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1591

670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 139306);