Finite Group Databasebeta

D13×#1367 #15774459

order3328
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productD13×#1367

Splittings

FittingC13×#1367 ⋊ C2
SylowC13 ⋊ C2×#1367

Subgroups

subgroupG/H
centerC2×C8D4×D13
commutatorC4×C13C22×C16
FrattiniC4×C8C22×D13
FittingC13×#1367C2
socleC22×C13C2×C4⋊C8
prime radicalC22×D13C4⋊C8
cosocleC4×C8×C13C23
hypercenter#1367D13
hypocenterC13C2×#1367
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ #1367

286 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 81108);