Finite Group Databasebeta

D13×#1425 #15783428

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

Aliases

direct productD13×#1425

Splittings

FittingC13×#1425 ⋊ C2
SylowC13 ⋊ C2×#1425

Subgroups

subgroupG/H
centerC4D13×D16
commutatorC13×C16C22×C4
FrattiniC2×C16C22×D13
FittingC13×#1425C2
socleC2×C13C2×#366
prime radicalC22×D13Q32
cosocleC2×C13×C16C23
hypercenter#1425D13
hypocenterC13C2×#1425
LCSG ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1425

182 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 81 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 90077);