Finite Group Databasebeta

D13×#2069 #15891634

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productD13×#2069

Splittings

FittingC13×#2069 ⋊ C2
SylowC13 ⋊ C2×#2069

Subgroups

subgroupG/H
centerC2D13×#396
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2069C2
socleC2×C13C2×#396
prime radicalC22×D4×D13C22
hypercenter#2069D13
hypocenterC13C2×#2069
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22×C4 ◁ #2069

1078 conjugacy classes of subgroups; only the 207 normal subgroups are shown.

normal subgroups only

This group has 1078 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, 198283);