Finite Group Databasebeta

D13×#1446 #15784667

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

direct productD13×#1446

Splittings

FittingC13×#1446 ⋊ C2
SylowC13 ⋊ C2×#1446

Subgroups

subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1446C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenter#1446D13
hypocenterC13C2×#1446
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1446

4830 conjugacy classes of subgroups; only the 763 normal subgroups are shown.

normal subgroups only

This group has 4830 conjugacy classes of subgroups — too many to draw. Only its 763 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 91316);