Finite Group Databasebeta

D13×#1406 #15783196

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

Aliases

direct productD13×#1406

Splittings

FittingC13×#1406 ⋊ C2
SylowC13 ⋊ C2×#1406

Subgroups

subgroupG/H
centerC2D13×#353
commutatorC42×C13C22×C4
Frattini#124C22×D13
FittingC13×#1406C2
socleC2×C13C2×#353
prime radicalD13×#496C2
cosocleC13×#124C23
hypercenter#1406D13
hypocenterC13C2×#1406
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #1406

468 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 61 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

112 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 89845);