Finite Group Databasebeta

D13×#1304 #15753237

order3328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C26

Aliases

direct productD13×#1304

Splittings

FittingC13×#1304 ⋊ C2
SylowC13 ⋊ C2×#1304

Subgroups

subgroupG/H
centerC22D13×#95
commutatorC23×C13C2×C42
FrattiniC25C22×D13
FittingC13×#1304C2
socleC22×C13C2×#95
prime radicalC25×D13C22
cosocleC25×C13C23
hypercenter#1304D13
hypocenterC13C2×#1304
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C25 ◁ #1304

2414 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 2414 conjugacy classes of subgroups — too many to draw. Only its 179 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

208 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 59886);