Finite Group Databasebeta

D13×#1391 #15777872

order3328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productD13×#1391

Splittings

FittingC13×#1391 ⋊ C2
SylowC13 ⋊ C2×#1391

Subgroups

subgroupG/H
centerC4D13×#99
commutatorC23×C13C2×C42
FrattiniC2×#41C22×D13
FittingC13×#1391C2
socleC2×C13C2×#342
prime radicalC2×#41×D13C22
cosocleC2×C13×#41C23
hypercenter#1391D13
hypocenterC13C2×#1391
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #1391

782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

208 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 84521);