Finite Group Databasebeta

D13×#1738 #15860337

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27

Aliases

direct productD13×#1738

Splittings

FittingC13×#1738 ⋊ C2
SylowC13 ⋊ C2×#1738

Subgroups

subgroupG/H
centerC2×C4C2×D4×D13
commutatorC4×C13C22×C42
FrattiniC22×C4C23×D13
FittingC13×#1738C2
socleC22×C13C22×C4⋊C4
prime radicalC24×D13Q8
cosocleC22×C4×C13C24
hypercenter#1738D13
hypocenterC13C2×#1738
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1738

2110 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, 166986);