Finite Group Databasebeta

D13×#1376 #15777770

order3328
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C24

Aliases

direct productD13×#1376

Splittings

FittingC13×#1376 ⋊ C2
SylowC13 ⋊ C2×#1376

Subgroups

subgroupG/H
centerC2×C8D4×D13
commutatorC4×C13C2×C4×C8
FrattiniC22×C8C22×D13
FittingC13×#1376C2
socleC22×C13C2×C4⋊C8
prime radicalC23×D13M16
cosocleC22×C8×C13C23
hypercenter#1376D13
hypocenterC13C2×#1376
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ #1376

670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 84419);