Finite Group Databasebeta

D13×#1747 #15860420

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct productD13×#1747

Splittings

FittingC13×#1747 ⋊ C2
SylowC13 ⋊ C2×#1747

Subgroups

subgroupG/H
centerC8C42×D13
commutatorC4×C13C22×C42
FrattiniC22×C4C23×D13
FittingC13×#1747C2
socleC2×C13C2×#376
prime radicalC23×D13#41
cosocleC22×C4×C13C24
hypercenter#1747D13
hypocenterC13C2×#1747
LCSG ▷ C4×C13 ▷ C13
UCSC1 ◁ C8 ◁ #1747

930 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

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, 167069);