Finite Group Databasebeta

D13×#2896 #16726455

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productD13×#2896

Splittings

FittingC13×#2896 ⋊ C2
SylowC13 ⋊ C2×#2896

Subgroups

subgroupG/H
centerC2×C4C2×D4×D13
commutatorC4×C13C24×C4
FrattiniC2×C4C24×D13
FittingC13×#2896C2
socleC22×C13C23×D4
prime radicalC22×#41×D13C2
cosocleC2×C4×C13C25
hypercenter#2896D13
hypocenterC13C2×#2896
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2896

5198 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, 1033104);