Finite Group Databasebeta

D13×#1312 #15771904

order3328
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4

Aliases

direct productD13×#1312

Splittings

FittingC13×#1312 ⋊ C2
SylowC13 ⋊ C2×#1312

Subgroups

subgroupG/H
center, FrattiniC4×C8C22×D13
commutatorC2×C13C2×C4×C16
FittingC13×#1312C2
socleC22×C13C2×C4×C8
prime radicalC22×D13C4×C8
cosocleC4×C8×C13C23
hypercenter#1312D13
hypocenterC13C2×#1312
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C4×C8 ◁ #1312

350 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 78553);