Finite Group Databasebeta

D13×#1361 #15774153

order3328
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productD13×#1361

Splittings

FittingC13×#1361 ⋊ C2
SylowC13 ⋊ C2×#1361

Subgroups

subgroupG/H
centerC22D13×#102
commutatorC2×C8×C13C22×C4
FrattiniC4×C8C22×D13
FittingC13×#1361C2
socleC22×C13C2×#102
prime radicalD13×#493C2
cosocleC4×C8×C13C23
hypercenter#1361D13
hypocenterC13C2×#1361
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1361

518 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 111 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) = 832

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 80802);