Finite Group Databasebeta

D13×#1423 #15783413

order3328
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productD13×#1423

Splittings

FittingC13×#1423 ⋊ C2
SylowC13 ⋊ C2×#1423

Subgroups

subgroupG/H
centerC22D13×D16
commutatorC13×C16C22×C4
FrattiniC2×C16C22×D13
FittingC13×#1423C2
socleC22×C13C2×D16
prime radicalC22×D13D16
cosocleC2×C13×C16C23
hypercenter#1423D13
hypocenterC13C2×#1423
LCSG ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1423

206 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 91 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) = 1664

Conjugacy classes & character table

304 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 90062);