Finite Group Databasebeta

D13×#2032 #15890355

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productD13×#2032

Splittings

FittingC13×#2032 ⋊ C2
SylowC13 ⋊ C2×#2032

Subgroups

subgroupG/H
centerC2D13×#393
commutator, cosocleC24×C13C24
FrattiniC24C23×D13
FittingC13×#2032C2
socleC2×C13C2×#393
prime radicalC22×D4×D13C22
hypercenter#2032D13
hypocenterC13C2×#2032
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C24 ◁ #2032

1434 conjugacy classes of subgroups; only the 207 normal subgroups are shown.

normal subgroups only

This group has 1434 conjugacy classes of subgroups — too many to draw. Only its 207 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 208

Conjugacy classes & character table

184 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 197004);